out := [[[1, 10, 6, 2, 1], [v < 0, u = (v^2+1)^(1/2), x = 1, y = -1, z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [-1, -1],
[-1, -1]]]], [[1, 10, 6, 2, 2], [v < 0, u = (v^2+1)^(1/2), x = 1, y = -1, z =
0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [-1,
-1], [0, 0]]]], [[1, 10, 6, 2, 3], [v < 0, u = (v^2+1)^(1/2), x = 1, y = -1, 0
< z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [-1
, -1], [1, 1]]]], [[2, 2, 4, 1, 1], [v = 0, u = -2^(1/2), x = 1, y < 0, z = z]
, [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1
], [0, 0]]]], [[3, 5, 7, 5, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x,
x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [2, 2], [4, 4], [-2, -2]]]], [[3, 5, 7, 5, 2], [0
< v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)
^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2]
, [4, 4], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 7, 5, 3], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2
) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [2, 2], [4, 4], [-1/4194304, -1/4194304]]]], [[3, 5, 7, 5, 4
], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, x-u^2+v^2+1 < y, z = (-u^2+v
^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
2, 2], [4, 4], [193151/262144, 772605/1048576]]]], [[3, 5, 7, 5, 5], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z
], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [4,
4], [2, 2]]]], [[3, 11, 1, 1, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1
/2)), x < -1, y < x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [3299097/
2097152, 3299097/2097152], [-2, -2], [-4, -4], [0, 0]]]], [[1, 5, 6, 1, 1], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y < u^2-v^2-2, z < -(-u^2+v^2+1)^(1
/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1],
[-3, -3], [-2, -2]]]], [[1, 5, 6, 1, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v)
, x = 1, y < u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
-1265743/1048576, -1265743/1048576], [1, 1], [-3, -3], [-772605/1048576, -\
1545209/2097152]]]], [[1, 5, 6, 1, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v),
x = 1, y < u^2-v^2-2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3, -\
3], [-1/4194304, -1/4194304]]]], [[1, 5, 6, 1, 4], [v < 0, And(-(v^2+1)^(1/2)
< u,u < v), x = 1, y < u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-\
1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3, -3], [193151/262144
, 772605/1048576]]]], [[1, 5, 6, 1, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v),
x = 1, y < u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [1, 1], [-3, -3], [2, 2]]]], [[2, 7, 4, 3,
1], [v = 0, And(0 < u,u < 1), x = u^2-1, 0 < y, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [1, 1], [-2, -2]]]], [[2, 7,
4, 3, 2], [v = 0, And(0 < u,u < 1), x = u^2-1, 0 < y, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [1, 1], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 4, 3, 3], [v = 0, And(0 < u,u < 1), x = u^2-1, 0
< y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1
/2, 1/2], [-3/4, -3/4], [1, 1], [-1/8388608, -1/8388608]]]], [[2, 7, 4, 3, 4],
[v = 0, And(0 < u,u < 1), x = u^2-1, 0 < y, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [1, 1], [908093/1048576, 
454047/524288]]]], [[2, 7, 4, 3, 5], [v = 0, And(0 < u,u < 1), x = u^2-1, 0 <
y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [1,
1], [2, 2]]]], [[3, 1, 2, 4, 1], [0 < v, u < -(v^2+2)^(1/2), x = -1, y = u^2-v
^2, z = z], [regular_chain, [[1, 1], [-3, -3], [-1, -1], [8, 8], [0, 0]]]], [[
3, 11, 1, 2, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x < -1, y =
x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/
2097152], [-2, -2], [-1297479/524288, -2594957/1048576], [0, 0]]]], [[1, 10, 6
, 3, 1], [v < 0, u = (v^2+1)^(1/2), x = 1, And(-1 < y,y < 1), z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [0, 0], [-\
1, -1]]]], [[1, 10, 6, 3, 2], [v < 0, u = (v^2+1)^(1/2), x = 1, And(-1 < y,y <
1), z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1
], [0, 0], [0, 0]]]], [[1, 10, 6, 3, 3], [v < 0, u = (v^2+1)^(1/2), x = 1, And
(-1 < y,y < 1), 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [1, 1], [0, 0], [1, 1]]]], [[2, 2, 4, 2, 1], [v = 0, u = -2^(1/2), x
= 1, y = 0, z = z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288
], [1, 1], [0, 0], [0, 0]]]], [[3, 5, 7, 4, 1], [0 < v, And(-(v^2+1)^(1/2) < u
,u < -v), 1 < x, y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [2666417/1048576, 1333209
/524288], [-2, -2]]]], [[3, 5, 7, 4, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v
), 1 < x, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[-1265743/1048576, -1265743/1048576], [2, 2], [2666417/1048576, 1333209/524288
], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 7, 4, 3], [0 < v, And(-(v^2
+1)^(1/2) < u,u < -v), 1 < x, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [2, 2], [2666417/1048576, 1333209/524288], [-1/4194304, -1/4194304]]
]], [[3, 5, 7, 4, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y = x-u^2
+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [2, 2], [2666417/1048576, 1333209/524288], [193151/262144, 
772605/1048576]]]], [[3, 5, 7, 4, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
1 < x, y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [2, 2], [2666417/1048576, 1333209/524288],
[2, 2]]]], [[3, 10, 7, 5, 1], [0 < v, u = (v^2+1)^(1/2), 1 < x, x < y, z < 0],
[regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [2, 2], [3, 3], [-1
, -1]]]], [[3, 10, 7, 5, 2], [0 < v, u = (v^2+1)^(1/2), 1 < x, x < y, z = 0],
[regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [2, 2], [3, 3], [0,
0]]]], [[3, 10, 7, 5, 3], [0 < v, u = (v^2+1)^(1/2), 1 < x, x < y, 0 < z], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [2, 2], [3, 3], [1,
1]]]], [[1, 1, 1, 1, 1], [v < 0, u < -(v^2+2)^(1/2), x < -1, y < x-u^2+v^2+1,
z = z], [regular_chain, [[-1, -1], [-3, -3], [-2, -2], [-10, -10], [0, 0]]]],
[[1, 5, 6, 2, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = u^2-v^2-2,
z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [-2, -2]]]], [
[1, 5, 6, 2, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = u^2-v^2-2,
z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [-772605/
1048576, -1545209/2097152]]]], [[1, 5, 6, 2, 3], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = 1, y = u^2-v^2-2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(
1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1
], [-3235683/2097152, -1617841/1048576], [-1/4194304, -1/4194304]]]], [[1, 5,
6, 2, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = u^2-v^2-2, z = (-u
^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [193151/262144, 772605
/1048576]]]], [[1, 5, 6, 2, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1,
y = u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [2,
2]]]], [[2, 7, 4, 2, 1], [v = 0, And(0 < u,u < 1), x = u^2-1, y = 0, z < -(-u^
2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [0, 0], [-2, -\
2]]]], [[2, 7, 4, 2, 2], [v = 0, And(0 < u,u < 1), x = u^2-1, y = 0, z = -(-u^
2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [0, 0], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 7, 4, 2, 3], [v = 0, And(0 < u,u <
1), x = u^2-1, y = 0, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [0, 0], [-1/8388608, -1/
8388608]]]], [[2, 7, 4, 2, 4], [v = 0, And(0 < u,u < 1), x = u^2-1, y = 0, z =
(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [0, 0], [
908093/1048576, 454047/524288]]]], [[2, 7, 4, 2, 5], [v = 0, And(0 < u,u < 1),
x = u^2-1, y = 0, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-\
3/4, -3/4], [0, 0], [2, 2]]]], [[3, 1, 2, 3, 1], [0 < v, u < -(v^2+2)^(1/2), x
= -1, And(-u^2+v^2 < y,y < u^2-v^2), z = z], [regular_chain, [[1, 1], [-3, -3]
, [-1, -1], [0, 0], [0, 0]]]], [[3, 11, 1, 3, 1], [0 < v, And((v^2+1)^(1/2) <
u,u < (v^2+2)^(1/2)), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [
regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [-2, -2], [0, 0],
[0, 0]]]], [[1, 10, 6, 4, 1], [v < 0, u = (v^2+1)^(1/2), x = 1, y = 1, z < 0],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [1, 1], [
-1, -1]]]], [[1, 10, 6, 4, 2], [v < 0, u = (v^2+1)^(1/2), x = 1, y = 1, z = 0]
, [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [1, 1],
[0, 0]]]], [[1, 10, 6, 4, 3], [v < 0, u = (v^2+1)^(1/2), x = 1, y = 1, 0 < z],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [1, 1], [
1, 1]]]], [[2, 2, 3, 4, 1], [v = 0, u = -2^(1/2), And(-1 < x,x < 1), y = 1-x,
z = z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [0, 0], [
1, 1], [0, 0]]]], [[3, 6, 1, 2, 1], [0 < v, u = -v, x < -1, y = x+1, z < -1],
[regular_chain, [[1, 1], [-1, -1], [-2, -2], [-1, -1], [-2, -2]]]], [[3, 6, 1,
2, 2], [0 < v, u = -v, x < -1, y = x+1, z = -1], [regular_chain, [[1, 1], [-1,
-1], [-2, -2], [-1, -1], [-1, -1]]]], [[3, 6, 1, 2, 3], [0 < v, u = -v, x < -1
, y = x+1, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [-\
1, -1], [0, 0]]]], [[3, 6, 1, 2, 4], [0 < v, u = -v, x < -1, y = x+1, z = 1],
[regular_chain, [[1, 1], [-1, -1], [-2, -2], [-1, -1], [1, 1]]]], [[3, 6, 1, 2
, 5], [0 < v, u = -v, x < -1, y = x+1, 1 < z], [regular_chain, [[1, 1], [-1, -\
1], [-2, -2], [-1, -1], [2, 2]]]], [[3, 10, 7, 4, 1], [0 < v, u = (v^2+1)^(1/2
), 1 < x, y = x, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [2, 2], [2, 2], [-1, -1]]]], [[3, 10, 7, 4, 2], [0 < v, u = (v^2+1)^
(1/2), 1 < x, y = x, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [2, 2], [2, 2], [0, 0]]]], [[3, 10, 7, 4, 3], [0 < v, u = (v^2+1)^(1
/2), 1 < x, y = x, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [2, 2], [2, 2], [1, 1]]]], [[1, 1, 1, 2, 1], [v < 0, u < -(v^2+2)^(1
/2), x < -1, y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [-3, -3], [-2
, -2], [-9, -9], [0, 0]]]], [[1, 5, 5, 4, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u
< v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [101115/131072, 808921/1048576], [-2, -2]]]], [[1, 5
, 5, 4, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y
= x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [101115/131072,
808921/1048576], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 5, 4, 3], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [
101115/131072, 808921/1048576], [-1/4194304, -1/4194304]]]], [[1, 5, 5, 4, 4],
[v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2
+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [479311/2097152, 479311/2097152], [101115/131072, 808921/
1048576], [193151/262144, 772605/1048576]]]], [[1, 5, 5, 4, 5], [v < 0, And(-(
v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, (-u^2+v^2+
1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576]
, [479311/2097152, 479311/2097152], [101115/131072, 808921/1048576], [2, 2]]]]
, [[2, 7, 5, 2, 1], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = u^2-x-\
1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [-7/
8, -7/8], [-2, -2]]]], [[2, 7, 5, 2, 2], [v = 0, And(0 < u,u < 1), And(u^2-1 <
x,x < 1), y = u^2-x-1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/
2], [1/8, 1/8], [-7/8, -7/8], [-1816187/2097152, -3632373/4194304]]]], [[2, 7,
5, 2, 3], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = u^2-x-1, And(-(-
u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [1
/8, 1/8], [-7/8, -7/8], [-1/8388608, -1/8388608]]]], [[2, 7, 5, 2, 4], [v = 0,
And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = u^2-x-1, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [-7/8, -7/8], [908093/1048576,
454047/524288]]]], [[2, 7, 5, 2, 5], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x
< 1), y = u^2-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [
1/8, 1/8], [-7/8, -7/8], [2, 2]]]], [[3, 1, 2, 2, 1], [0 < v, u < -(v^2+2)^(1/
2), x = -1, y = -u^2+v^2, z = z], [regular_chain, [[1, 1], [-3, -3], [-1, -1],
[-8, -8], [0, 0]]]], [[3, 11, 1, 4, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2
+2)^(1/2)), x < -1, y = u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3299097
/2097152, 3299097/2097152], [-2, -2], [2594957/1048576, 1297479/524288], [0, 0
]]]], [[1, 10, 6, 5, 1], [v < 0, u = (v^2+1)^(1/2), x = 1, 1 < y, z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [2, 2], [-\
1, -1]]]], [[1, 10, 6, 5, 2], [v < 0, u = (v^2+1)^(1/2), x = 1, 1 < y, z = 0],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [2, 2], [
0, 0]]]], [[1, 10, 6, 5, 3], [v < 0, u = (v^2+1)^(1/2), x = 1, 1 < y, 0 < z],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1, 1], [2, 2], [
1, 1]]]], [[2, 2, 3, 5, 1], [v = 0, u = -2^(1/2), And(-1 < x,x < 1), 1-x < y,
z = z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [0, 0], [
2, 2], [0, 0]]]], [[3, 6, 1, 1, 1], [0 < v, u = -v, x < -1, y < x+1, z < -1],
[regular_chain, [[1, 1], [-1, -1], [-2, -2], [-2, -2], [-2, -2]]]], [[3, 6, 1,
1, 2], [0 < v, u = -v, x < -1, y < x+1, z = -1], [regular_chain, [[1, 1], [-1,
-1], [-2, -2], [-2, -2], [-1, -1]]]], [[3, 6, 1, 1, 3], [0 < v, u = -v, x < -1
, y < x+1, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [-\
2, -2], [0, 0]]]], [[3, 6, 1, 1, 4], [0 < v, u = -v, x < -1, y < x+1, z = 1],
[regular_chain, [[1, 1], [-1, -1], [-2, -2], [-2, -2], [1, 1]]]], [[3, 6, 1, 1
, 5], [0 < v, u = -v, x < -1, y < x+1, 1 < z], [regular_chain, [[1, 1], [-1, -\
1], [-2, -2], [-2, -2], [2, 2]]]], [[3, 10, 7, 3, 1], [0 < v, u = (v^2+1)^(1/2
), 1 < x, And(-x < y,y < x), z < 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [2, 2], [0, 0], [-1, -1]]]], [[3, 10, 7, 3, 2], [0 < v, u =
(v^2+1)^(1/2), 1 < x, And(-x < y,y < x), z = 0], [regular_chain, [[1, 1], [
741455/524288, 1482911/1048576], [2, 2], [0, 0], [0, 0]]]], [[3, 10, 7, 3, 3],
[0 < v, u = (v^2+1)^(1/2), 1 < x, And(-x < y,y < x), 0 < z], [regular_chain, [
[1, 1], [741455/524288, 1482911/1048576], [2, 2], [0, 0], [1, 1]]]], [[1, 1, 1
, 3, 1], [v < 0, u < -(v^2+2)^(1/2), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x
-1), z = z], [regular_chain, [[-1, -1], [-3, -3], [-2, -2], [0, 0], [0, 0]]]],
[[1, 5, 5, 5, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x <
1), x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [2, 2],
[-2, -2]]]], [[1, 5, 5, 5, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-
v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/
2097152], [2, 2], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 5, 5, 3], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [2,
2], [-1/4194304, -1/4194304]]]], [[1, 5, 5, 5, 4], [v < 0, And(-(v^2+1)^(1/2)
< u,u < v), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)]
, [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [2, 2], [193151/262144, 772605/1048576]]]], [[1, 5,
5, 5, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), x-u
^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [2, 2], [2, 2]]]
], [[2, 7, 5, 1, 1], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y < u^2-x
-1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [-2
, -2], [-2, -2]]]], [[2, 7, 5, 1, 2], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,
x < 1), y < u^2-x-1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2]
, [1/8, 1/8], [-2, -2], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 5, 1,
3], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y < u^2-x-1, And(-(-u^2+1)
^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/
8], [-2, -2], [-1/8388608, -1/8388608]]]], [[2, 7, 5, 1, 4], [v = 0, And(0 < u
,u < 1), And(u^2-1 < x,x < 1), y < u^2-x-1, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [-2, -2], [908093/1048576, 
454047/524288]]]], [[2, 7, 5, 1, 5], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x
< 1), y < u^2-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [
1/8, 1/8], [-2, -2], [2, 2]]]], [[3, 1, 2, 1, 1], [0 < v, u < -(v^2+2)^(1/2),
x = -1, y < -u^2+v^2, z = z], [regular_chain, [[1, 1], [-3, -3], [-1, -1], [-9
, -9], [0, 0]]]], [[3, 11, 1, 5, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)
^(1/2)), x < -1, u^2-v^2-x-1 < y, z = z], [regular_chain, [[1, 1], [3299097/
2097152, 3299097/2097152], [-2, -2], [4, 4], [0, 0]]]], [[1, 1, 1, 4, 1], [v <
0, u < -(v^2+2)^(1/2), x < -1, y = u^2-v^2-x-1, z = z], [regular_chain, [[-1,
-1], [-3, -3], [-2, -2], [9, 9], [0, 0]]]], [[1, 5, 6, 5, 1], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x = 1, -u^2+v^2+2 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [3, 3]
, [-2, -2]]]], [[1, 5, 6, 5, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1,
-u^2+v^2+2 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743
/1048576, -1265743/1048576], [1, 1], [3, 3], [-772605/1048576, -1545209/
2097152]]]], [[1, 5, 6, 5, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, -
u^2+v^2+2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [3, 3]
, [-1/4194304, -1/4194304]]]], [[1, 5, 6, 5, 4], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = 1, -u^2+v^2+2 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1
, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [3, 3], [193151/262144, 
772605/1048576]]]], [[1, 5, 6, 5, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x
= 1, -u^2+v^2+2 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [1, 1], [3, 3], [2, 2]]]], [[2, 7, 5, 4, 1
], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = x-u^2+1, z < -(-u^2+1)^
(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [7/8, 7/8], [-2, -2]]
]], [[2, 7, 5, 4, 2], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = x-u^
2+1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [7
/8, 7/8], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 5, 4, 3], [v = 0, 
And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z
< (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [7/8, 7/8
], [-1/8388608, -1/8388608]]]], [[2, 7, 5, 4, 4], [v = 0, And(0 < u,u < 1), 
And(u^2-1 < x,x < 1), y = x-u^2+1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0
], [1/2, 1/2], [1/8, 1/8], [7/8, 7/8], [908093/1048576, 454047/524288]]]], [[2
, 7, 5, 4, 5], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), y = x-u^2+1, (-
u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [7/8, 7/8]
, [2, 2]]]], [[3, 1, 3, 3, 1], [0 < v, u < -(v^2+2)^(1/2), And(-1 < x,x < 1),
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[1, 1], [-3, -3
], [0, 0], [0, 0], [0, 0]]]], [[3, 11, 2, 1, 1], [0 < v, And((v^2+1)^(1/2) < u
,u < (v^2+2)^(1/2)), x = -1, y < -u^2+v^2, z = z], [regular_chain, [[1, 1], [
3299097/2097152, 3299097/2097152], [-1, -1], [-3, -3], [0, 0]]]], [[1, 10, 5,
3, 1], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y < x), z < 0],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1/2, 1/2], [0, 0
], [-1, -1]]]], [[1, 10, 5, 3, 2], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1)
, And(-x < y,y < x), z = 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [1/2, 1/2], [0, 0], [0, 0]]]], [[1, 10, 5, 3, 3], [v < 0, u
= (v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y < x), 0 < z], [regular_chain,
[[-1, -1], [741455/524288, 1482911/1048576], [1/2, 1/2], [0, 0], [1, 1]]]], [[
2, 2, 3, 2, 1], [v = 0, u = -2^(1/2), And(-1 < x,x < 1), y = x-1, z = z], [
regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [0, 0], [-1, -1],
[0, 0]]]], [[3, 5, 7, 1, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y
< u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [2, 2], [-4, -4], [-2, -2]]]], [[3, 5, 7, 1, 2], [
0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y < u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2,
2], [-4, -4], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 7, 1, 3], [0 < v
, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1
/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576,
-1265743/1048576], [2, 2], [-4, -4], [-1/4194304, -1/4194304]]]], [[3, 5, 7, 1
, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y < u^2-v^2-x-1, z = (-u^
2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576]
, [2, 2], [-4, -4], [193151/262144, 772605/1048576]]]], [[3, 5, 7, 1, 5], [0 <
v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2)
< z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [
-4, -4], [2, 2]]]], [[3, 10, 7, 2, 1], [0 < v, u = (v^2+1)^(1/2), 1 < x, y = -
x, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [2, 2],
[-2, -2], [-1, -1]]]], [[3, 10, 7, 2, 2], [0 < v, u = (v^2+1)^(1/2), 1 < x, y
= -x, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [2, 2
], [-2, -2], [0, 0]]]], [[3, 10, 7, 2, 3], [0 < v, u = (v^2+1)^(1/2), 1 < x, y
= -x, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [2, 2
], [-2, -2], [1, 1]]]], [[1, 1, 1, 5, 1], [v < 0, u < -(v^2+2)^(1/2), x < -1,
u^2-v^2-x-1 < y, z = z], [regular_chain, [[-1, -1], [-3, -3], [-2, -2], [10, 
10], [0, 0]]]], [[1, 5, 7, 1, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x
, y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [2, 2], [-4, -4], [-2, -2]]]], [[1, 5, 7,
1, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y < u^2-v^2-x-1, z = -(-u
^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [2, 2], [-4, -4], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 7,
1, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y < u^2-v^2-x-1, And(-(-u
^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [2, 2], [-4, -4], [-1/4194304, -1/4194304]
]]], [[1, 5, 7, 1, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y < u^2-v
^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576,
-1265743/1048576], [2, 2], [-4, -4], [193151/262144, 772605/1048576]]]], [[1,
5, 7, 1, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y < u^2-v^2-x-1, (-
u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [2, 2], [-4, -4], [2, 2]]]], [[2, 7, 5, 3, 1], [v = 0, And(0 < u,u <
1), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,y < x-u^2+1), z < -(-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [0, 0], [-2, -2]]]], [[2, 7,
5, 3, 2], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,y <
x-u^2+1), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8
], [0, 0], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 5, 3, 3], [v = 0,
And(0 < u,u < 1), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,y < x-u^2+1), And(-(-u
^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [1/
8, 1/8], [0, 0], [-1/8388608, -1/8388608]]]], [[2, 7, 5, 3, 4], [v = 0, And(0
< u,u < 1), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,y < x-u^2+1), z = (-u^2+1)^(
1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [0, 0], [908093/
1048576, 454047/524288]]]], [[2, 7, 5, 3, 5], [v = 0, And(0 < u,u < 1), And(u^
2-1 < x,x < 1), And(u^2-x-1 < y,y < x-u^2+1), (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [0, 0], [2, 2]]]], [[3, 1, 3,
2, 1], [0 < v, u < -(v^2+2)^(1/2), And(-1 < x,x < 1), y = x-u^2+v^2+1, z = z],
[regular_chain, [[1, 1], [-3, -3], [0, 0], [-7, -7], [0, 0]]]], [[3, 11, 2, 2,
1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -1, y = -u^2+v^2, z
= z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [-1, -1], [
-773191/524288, -1546381/1048576], [0, 0]]]], [[1, 10, 5, 4, 1], [v < 0, u = (
v^2+1)^(1/2), And(0 < x,x < 1), y = x, z < 0], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [1/2, 1/2], [1/2, 1/2], [-1, -1]]]], [[1, 10,
5, 4, 2], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1), y = x, z = 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1/2, 1/2], [1/2,
1/2], [0, 0]]]], [[1, 10, 5, 4, 3], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1
), y = x, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576],
[1/2, 1/2], [1/2, 1/2], [1, 1]]]], [[2, 2, 3, 3, 1], [v = 0, u = -2^(1/2), And
(-1 < x,x < 1), And(x-1 < y,y < 1-x), z = z], [regular_chain, [[0, 0], [-\
1482911/1048576, -741455/524288], [0, 0], [0, 0], [0, 0]]]], [[3, 5, 6, 5, 1],
[0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, -u^2+v^2+2 < y, z < -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1,
1], [3, 3], [-2, -2]]]], [[3, 5, 6, 5, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u <
-v), x = 1, -u^2+v^2+2 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[-1265743/1048576, -1265743/1048576], [1, 1], [3, 3], [-772605/1048576, -\
1545209/2097152]]]], [[3, 5, 6, 5, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
x = 1, -u^2+v^2+2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [3, 3],
[-1/4194304, -1/4194304]]]], [[3, 5, 6, 5, 4], [0 < v, And(-(v^2+1)^(1/2) < u,
u < -v), x = 1, -u^2+v^2+2 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [-1265743/1048576, -1265743/1048576], [1, 1], [3, 3], [193151/262144, 
772605/1048576]]]], [[3, 5, 6, 5, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
x = 1, -u^2+v^2+2 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [1, 1], [3, 3], [2, 2]]]], [[3, 10, 7, 1,
1], [0 < v, u = (v^2+1)^(1/2), 1 < x, y < -x, z < 0], [regular_chain, [[1, 1],
[741455/524288, 1482911/1048576], [2, 2], [-3, -3], [-1, -1]]]], [[3, 10, 7, 1
, 2], [0 < v, u = (v^2+1)^(1/2), 1 < x, y < -x, z = 0], [regular_chain, [[1, 1
], [741455/524288, 1482911/1048576], [2, 2], [-3, -3], [0, 0]]]], [[3, 10, 7,
1, 3], [0 < v, u = (v^2+1)^(1/2), 1 < x, y < -x, 0 < z], [regular_chain, [[1,
1], [741455/524288, 1482911/1048576], [2, 2], [-3, -3], [1, 1]]]], [[1, 1, 2,
1, 1], [v < 0, u < -(v^2+2)^(1/2), x = -1, y < -u^2+v^2, z = z], [
regular_chain, [[-1, -1], [-3, -3], [-1, -1], [-9, -9], [0, 0]]]], [[1, 5, 6,
3, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, And(u^2-v^2-2 < y,y < -u^
2+v^2+2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [1, 1], [0, 0], [-2, -2]]]], [[1, 5, 6, 3, 2], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2),
z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [1, 1], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[1,
5, 6, 3, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, And(u^2-v^2-2 < y,y
< -u^2+v^2+2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [0, 0]
, [-1/4194304, -1/4194304]]]], [[1, 5, 6, 3, 4], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [0, 0]
, [193151/262144, 772605/1048576]]]], [[1, 5, 6, 3, 5], [v < 0, And(-(v^2+1)^(
1/2) < u,u < v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), (-u^2+v^2+1)^(1/2)
< z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1],
[0, 0], [2, 2]]]], [[2, 7, 6, 1, 1], [v = 0, And(0 < u,u < 1), x = 1, y < u^2-\
2, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-3, -3]
, [-2, -2]]]], [[2, 7, 6, 1, 2], [v = 0, And(0 < u,u < 1), x = 1, y < u^2-2, z
= -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-3, -3], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 7, 6, 1, 3], [v = 0, And(0 < u,u <
1), x = 1, y < u^2-2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-3, -3], [-1/8388608, -1/8388608]
]]], [[2, 7, 6, 1, 4], [v = 0, And(0 < u,u < 1), x = 1, y < u^2-2, z = (-u^2+1
)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-3, -3], [908093/
1048576, 454047/524288]]]], [[2, 7, 6, 1, 5], [v = 0, And(0 < u,u < 1), x = 1,
y < u^2-2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [
-3, -3], [2, 2]]]], [[3, 1, 3, 1, 1], [0 < v, u < -(v^2+2)^(1/2), And(-1 < x,x
< 1), y < x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-3, -3], [0, 0], [-8,
-8], [0, 0]]]], [[3, 11, 2, 3, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(
1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z = z], [regular_chain, [[1, 1],
[3299097/2097152, 3299097/2097152], [-1, -1], [0, 0], [0, 0]]]], [[1, 10, 5, 5
, 1], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1), x < y, z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1/2, 1/2], [2, 2]
, [-1, -1]]]], [[1, 10, 5, 5, 2], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1),
x < y, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1
/2, 1/2], [2, 2], [0, 0]]]], [[1, 10, 5, 5, 3], [v < 0, u = (v^2+1)^(1/2), And
(0 < x,x < 1), x < y, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [1/2, 1/2], [2, 2], [1, 1]]]], [[2, 2, 2, 5, 1], [v = 0, u =
-2^(1/2), x = -1, 2 < y, z = z], [regular_chain, [[0, 0], [-1482911/1048576, -\
741455/524288], [-1, -1], [3, 3], [0, 0]]]], [[3, 5, 7, 3, 1], [0 < v, And(-(v
^2+1)^(1/2) < u,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u
^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576
], [2, 2], [0, 0], [-2, -2]]]], [[3, 5, 7, 3, 2], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [0,
0], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 7, 3, 3], [0 < v, And(-(v^
2+1)^(1/2) < u,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^
2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [2, 2], [0, 0], [-1/4194304, -1/4194304]]]
], [[3, 5, 7, 3, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, And(u^2-v^
2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[-1265743/1048576, -1265743/1048576], [2, 2], [0, 0], [193151/262144, 772605/
1048576]]]], [[3, 5, 7, 3, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x,
And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [0, 0], [2, 2]]]], [[3,
10, 6, 5, 1], [0 < v, u = (v^2+1)^(1/2), x = 1, 1 < y, z < 0], [regular_chain,
[[1, 1], [741455/524288, 1482911/1048576], [1, 1], [2, 2], [-1, -1]]]], [[3, 
10, 6, 5, 2], [0 < v, u = (v^2+1)^(1/2), x = 1, 1 < y, z = 0], [regular_chain,
[[1, 1], [741455/524288, 1482911/1048576], [1, 1], [2, 2], [0, 0]]]], [[3, 10,
6, 5, 3], [0 < v, u = (v^2+1)^(1/2), x = 1, 1 < y, 0 < z], [regular_chain, [[1
, 1], [741455/524288, 1482911/1048576], [1, 1], [2, 2], [1, 1]]]], [[1, 1, 2,
2, 1], [v < 0, u < -(v^2+2)^(1/2), x = -1, y = -u^2+v^2, z = z], [
regular_chain, [[-1, -1], [-3, -3], [-1, -1], [-8, -8], [0, 0]]]], [[1, 5, 6,
4, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = -u^2+v^2+2, z < -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [1, 1], [1617841/1048576, 808921/524288], [-2, -2]]]], [[1, 5, 6, 4,
2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = -u^2+v^2+2, z = -(-u^2+v
^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576],
[1, 1], [1617841/1048576, 808921/524288], [-772605/1048576, -1545209/2097152]]
]], [[1, 5, 6, 4, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = -u^2+v
^2+2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[
-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [1617841/1048576, 
808921/524288], [-1/4194304, -1/4194304]]]], [[1, 5, 6, 4, 4], [v < 0, And(-(v
^2+1)^(1/2) < u,u < v), x = 1, y = -u^2+v^2+2, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [1, 1], [
1617841/1048576, 808921/524288], [193151/262144, 772605/1048576]]]], [[1, 5, 6
, 4, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = 1, y = -u^2+v^2+2, (-u^2+v
^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [1, 1], [1617841/1048576, 808921/524288], [2, 2]]]], [[2, 7, 5, 5, 1
], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), x-u^2+1 < y, z < -(-u^2+1)^
(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [2, 2], [-2, -2]]]],
[[2, 7, 5, 5, 2], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x < 1), x-u^2+1 < y,
z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [2, 2],
[-1816187/2097152, -3632373/4194304]]]], [[2, 7, 5, 5, 3], [v = 0, And(0 < u,u
< 1), And(u^2-1 < x,x < 1), x-u^2+1 < y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^
(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [2, 2], [-1/8388608,
-1/8388608]]]], [[2, 7, 5, 5, 4], [v = 0, And(0 < u,u < 1), And(u^2-1 < x,x <
1), x-u^2+1 < y, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1/
8, 1/8], [2, 2], [908093/1048576, 454047/524288]]]], [[2, 7, 5, 5, 5], [v = 0,
And(0 < u,u < 1), And(u^2-1 < x,x < 1), x-u^2+1 < y, (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [1/2, 1/2], [1/8, 1/8], [2, 2], [2, 2]]]], [[3, 1, 2,
5, 1], [0 < v, u < -(v^2+2)^(1/2), x = -1, u^2-v^2 < y, z = z], [regular_chain
, [[1, 1], [-3, -3], [-1, -1], [9, 9], [0, 0]]]], [[3, 11, 2, 4, 1], [0 < v, 
And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -1, y = u^2-v^2, z = z], [
regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [-1, -1], [1546381
/1048576, 773191/524288], [0, 0]]]], [[1, 10, 6, 1, 1], [v < 0, u = (v^2+1)^(1
/2), x = 1, y < -1, z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911
/1048576], [1, 1], [-2, -2], [-1, -1]]]], [[1, 10, 6, 1, 2], [v < 0, u = (v^2+
1)^(1/2), x = 1, y < -1, z = 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [1, 1], [-2, -2], [0, 0]]]], [[1, 10, 6, 1, 3], [v < 0, u =
(v^2+1)^(1/2), x = 1, y < -1, 0 < z], [regular_chain, [[-1, -1], [741455/
524288, 1482911/1048576], [1, 1], [-2, -2], [1, 1]]]], [[2, 2, 3, 1, 1], [v =
0, u = -2^(1/2), And(-1 < x,x < 1), y < x-1, z = z], [regular_chain, [[0, 0],
[-1482911/1048576, -741455/524288], [0, 0], [-2, -2], [0, 0]]]], [[3, 5, 7, 2,
1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y = u^2-v^2-x-1, z < -(-u^2
+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576],
[2, 2], [-5332835/2097152, -2666417/1048576], [-2, -2]]]], [[3, 5, 7, 2, 2], [
0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y = u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2,
2], [-5332835/2097152, -2666417/1048576], [-772605/1048576, -1545209/2097152]]
]], [[3, 5, 7, 2, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y = u^2-v
^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain,
[[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [-5332835/2097152, -\
2666417/1048576], [-1/4194304, -1/4194304]]]], [[3, 5, 7, 2, 4], [0 < v, And(-
(v^2+1)^(1/2) < u,u < -v), 1 < x, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [2, 2], [-\
5332835/2097152, -2666417/1048576], [193151/262144, 772605/1048576]]]], [[3, 5
, 7, 2, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), 1 < x, y = u^2-v^2-x-1, (-
u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [2, 2], [-5332835/2097152, -2666417/1048576], [2, 2]]]], [[3, 10, 6,
4, 1], [0 < v, u = (v^2+1)^(1/2), x = 1, y = 1, z < 0], [regular_chain, [[1, 1
], [741455/524288, 1482911/1048576], [1, 1], [1, 1], [-1, -1]]]], [[3, 10, 6,
4, 2], [0 < v, u = (v^2+1)^(1/2), x = 1, y = 1, z = 0], [regular_chain, [[1, 1
], [741455/524288, 1482911/1048576], [1, 1], [1, 1], [0, 0]]]], [[3, 10, 6, 4,
3], [0 < v, u = (v^2+1)^(1/2), x = 1, y = 1, 0 < z], [regular_chain, [[1, 1],
[741455/524288, 1482911/1048576], [1, 1], [1, 1], [1, 1]]]], [[1, 11, 1, 1, 1]
, [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x < -1, y < x-u^2+v^2+1, z
= z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [-2, -2],
[-4, -4], [0, 0]]]], [[2, 3, 1, 2, 1], [v = 0, And(-2^(1/2) < u,u < -1), x < -\
1, y = x-u^2+1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/
1048576], [-2, -2], [-2576463/1048576, -1288231/524288], [0, 0]]]], [[3, 5, 6,
1, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, y < u^2-v^2-2, z < -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576]
, [1, 1], [-3, -3], [-2, -2]]]], [[3, 5, 6, 1, 2], [0 < v, And(-(v^2+1)^(1/2)
< u,u < -v), x = 1, y < u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3, -3], [-772605/
1048576, -1545209/2097152]]]], [[3, 5, 6, 1, 3], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), x = 1, y < u^2-v^2-2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^
(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1]
, [-3, -3], [-1/4194304, -1/4194304]]]], [[3, 5, 6, 1, 4], [0 < v, And(-(v^2+1
)^(1/2) < u,u < -v), x = 1, y < u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3, -3]
, [193151/262144, 772605/1048576]]]], [[3, 5, 6, 1, 5], [0 < v, And(-(v^2+1)^(
1/2) < u,u < -v), x = 1, y < u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3, -3]
, [2, 2]]]], [[3, 10, 6, 2, 1], [0 < v, u = (v^2+1)^(1/2), x = 1, y = -1, z <
0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1, 1], [-1, -1
], [-1, -1]]]], [[3, 10, 6, 2, 2], [0 < v, u = (v^2+1)^(1/2), x = 1, y = -1, z
= 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1, 1], [-1,
-1], [0, 0]]]], [[3, 10, 6, 2, 3], [0 < v, u = (v^2+1)^(1/2), x = 1, y = -1, 0
< z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1, 1], [-1,
-1], [1, 1]]]], [[1, 1, 2, 4, 1], [v < 0, u < -(v^2+2)^(1/2), x = -1, y = u^2-
v^2, z = z], [regular_chain, [[-1, -1], [-3, -3], [-1, -1], [8, 8], [0, 0]]]],
[[1, 5, 7, 5, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, x-u^2+v^2+1 <
y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [2, 2], [4, 4], [-2, -2]]]], [[1, 5, 7, 5, 2], [v < 0, And(-
(v^2+1)^(1/2) < u,u < v), 1 < x, x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [4, 4]
, [-772605/1048576, -1545209/2097152]]]], [[1, 5, 7, 5, 3], [v < 0, And(-(v^2+
1)^(1/2) < u,u < v), 1 < x, x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (
-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [2, 2], [4, 4], [-1/4194304, -1/4194304]]]], [[1, 5, 7, 5, 4], [v <
0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/
2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2],
[4, 4], [193151/262144, 772605/1048576]]]], [[1, 5, 7, 5, 5], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), 1 < x, x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [4, 4]
, [2, 2]]]], [[2, 7, 2, 4, 1], [v = 0, And(0 < u,u < 1), x = -1, y = u^2, z <
-(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [1/4, 1/4], [
-2, -2]]]], [[2, 7, 2, 4, 2], [v = 0, And(0 < u,u < 1), x = -1, y = u^2, z = -
(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [1/4, 1/4], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 7, 2, 4, 3], [v = 0, And(0 < u,u <
1), x = -1, y = u^2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [1/4, 1/4], [-1/8388608, -1/
8388608]]]], [[2, 7, 2, 4, 4], [v = 0, And(0 < u,u < 1), x = -1, y = u^2, z =
(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [1/4, 1/4], [
908093/1048576, 454047/524288]]]], [[2, 7, 2, 4, 5], [v = 0, And(0 < u,u < 1),
x = -1, y = u^2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-1
, -1], [1/4, 1/4], [2, 2]]]], [[2, 11, 7, 5, 1], [v = 0, 2^(1/2) < u, u^2-1 <
x, x-u^2+1 < y, z = z], [regular_chain, [[0, 0], [3, 3], [9, 9], [2, 2], [0, 0
]]]], [[3, 11, 3, 1, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And
(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [
3299097/2097152, 3299097/2097152], [-550771/2097152, -550771/2097152], [-2, -2
], [0, 0]]]], [[1, 10, 7, 5, 1], [v < 0, u = (v^2+1)^(1/2), 1 < x, x < y, z <
0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [3, 3
], [-1, -1]]]], [[1, 10, 7, 5, 2], [v < 0, u = (v^2+1)^(1/2), 1 < x, x < y, z
= 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [3,
3], [0, 0]]]], [[1, 10, 7, 5, 3], [v < 0, u = (v^2+1)^(1/2), 1 < x, x < y, 0 <
z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [3, 3
], [1, 1]]]], [[2, 3, 1, 1, 1], [v = 0, And(-2^(1/2) < u,u < -1), x < -1, y <
x-u^2+1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576]
, [-2, -2], [-4, -4], [0, 0]]]], [[3, 5, 6, 2, 1], [0 < v, And(-(v^2+1)^(1/2)
< u,u < -v), x = 1, y = u^2-v^2-2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3235683/2097152, -\
1617841/1048576], [-2, -2]]]], [[3, 5, 6, 2, 2], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), x = 1, y = u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1
, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3235683/2097152, -\
1617841/1048576], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 6, 2, 3], [0
< v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, y = u^2-v^2-2, And(-(-u^2+v^2+1)^(
1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576,
-1265743/1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [-1/4194304,
-1/4194304]]]], [[3, 5, 6, 2, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x =
1, y = u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [
193151/262144, 772605/1048576]]]], [[3, 5, 6, 2, 5], [0 < v, And(-(v^2+1)^(1/2
) < u,u < -v), x = 1, y = u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [-3235683/2097152, -\
1617841/1048576], [2, 2]]]], [[3, 10, 6, 3, 1], [0 < v, u = (v^2+1)^(1/2), x =
1, And(-1 < y,y < 1), z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911
/1048576], [1, 1], [0, 0], [-1, -1]]]], [[3, 10, 6, 3, 2], [0 < v, u = (v^2+1)
^(1/2), x = 1, And(-1 < y,y < 1), z = 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [1, 1], [0, 0], [0, 0]]]], [[3, 10, 6, 3, 3], [0 < v
, u = (v^2+1)^(1/2), x = 1, And(-1 < y,y < 1), 0 < z], [regular_chain, [[1, 1]
, [741455/524288, 1482911/1048576], [1, 1], [0, 0], [1, 1]]]], [[1, 1, 2, 3, 1
], [v < 0, u < -(v^2+2)^(1/2), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z = z],
[regular_chain, [[-1, -1], [-3, -3], [-1, -1], [0, 0], [0, 0]]]], [[1, 5, 7, 4
, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = x-u^2+v^2+1, z < -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [2, 2], [2666417/1048576, 1333209/524288], [-2, -2]]]], [[1, 5, 7, 4
, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = x-u^2+v^2+1, z = -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [2, 2], [2666417/1048576, 1333209/524288], [-772605/1048576, -\
1545209/2097152]]]], [[1, 5, 7, 4, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v),
1 < x, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))],
[regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [
2666417/1048576, 1333209/524288], [-1/4194304, -1/4194304]]]], [[1, 5, 7, 4, 4
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = x-u^2+v^2+1, z = (-u^2+v^
2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576],
[2, 2], [2666417/1048576, 1333209/524288], [193151/262144, 772605/1048576]]]],
[[1, 5, 7, 4, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = x-u^2+v^2+
1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [2, 2], [2666417/1048576, 1333209/524288], [2, 2]]]], [[2, 7
, 2, 5, 1], [v = 0, And(0 < u,u < 1), x = -1, u^2 < y, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [2, 2], [-2, -2]]]], [[2, 7, 2,
5, 2], [v = 0, And(0 < u,u < 1), x = -1, u^2 < y, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [2, 2], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 2, 5, 3], [v = 0, And(0 < u,u < 1), x = -1, u^2 <
y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2
, 1/2], [-1, -1], [2, 2], [-1/8388608, -1/8388608]]]], [[2, 7, 2, 5, 4], [v =
0, And(0 < u,u < 1), x = -1, u^2 < y, z = (-u^2+1)^(1/2)], [regular_chain, [[0
, 0], [1/2, 1/2], [-1, -1], [2, 2], [908093/1048576, 454047/524288]]]], [[2, 7
, 2, 5, 5], [v = 0, And(0 < u,u < 1), x = -1, u^2 < y, (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [2, 2], [2, 2]]]], [[3, 1, 1, 1,
1], [0 < v, u < -(v^2+2)^(1/2), x < -1, y < x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [-3, -3], [-2, -2], [-10, -10], [0, 0]]]], [[3, 11, 2,
5, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -1, u^2-v^2 < y,
z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [-1, -1],
[3, 3], [0, 0]]]], [[1, 11, 1, 3, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2
)^(1/2)), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain
, [[-1, -1], [3299097/2097152, 3299097/2097152], [-2, -2], [0, 0], [0, 0]]]],
[[2, 2, 5, 5, 1], [v = 0, u = -2^(1/2), 1 < x, x-1 < y, z = z], [regular_chain
, [[0, 0], [-1482911/1048576, -741455/524288], [2, 2], [2, 2], [0, 0]]]], [[3,
5, 6, 3, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, And(u^2-v^2-2 < y,
y < -u^2+v^2+2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [1, 1], [0, 0], [-2, -2]]]], [[3, 5, 6, 3, 2], [0
< v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2),
z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743
/1048576], [1, 1], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 6,
3, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, And(u^2-v^2-2 < y,y < -u
^2+v^2+2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [0, 0],
[-1/4194304, -1/4194304]]]], [[3, 5, 6, 3, 4], [0 < v, And(-(v^2+1)^(1/2) < u,
u < -v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [0, 0],
[193151/262144, 772605/1048576]]]], [[3, 5, 6, 3, 5], [0 < v, And(-(v^2+1)^(1/
2) < u,u < -v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), (-u^2+v^2+1)^(1/2) <
z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [0,
0], [2, 2]]]], [[3, 10, 5, 5, 1], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1),
x < y, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1/2
, 1/2], [2, 2], [-1, -1]]]], [[3, 10, 5, 5, 2], [0 < v, u = (v^2+1)^(1/2), And
(0 < x,x < 1), x < y, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911
/1048576], [1/2, 1/2], [2, 2], [0, 0]]]], [[3, 10, 5, 5, 3], [0 < v, u = (v^2+
1)^(1/2), And(0 < x,x < 1), x < y, 0 < z], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [1/2, 1/2], [2, 2], [1, 1]]]], [[1, 1, 3, 1, 1], [v
< 0, u < -(v^2+2)^(1/2), And(-1 < x,x < 1), y < x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [-3, -3], [0, 0], [-8, -8], [0, 0]]]], [[1, 5, 7, 3,
1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^
2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [2, 2], [0, 0], [-2, -2]]]], [[1, 5, 7, 3, 2], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1
), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [2, 2], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[1,
5, 7, 3, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, And(u^2-v^2-x-1 < y
,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [0, 0]
, [-1/4194304, -1/4194304]]]], [[1, 5, 7, 3, 4], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)]
, [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [0,
0], [193151/262144, 772605/1048576]]]], [[1, 5, 7, 3, 5], [v < 0, And(-(v^2+1)
^(1/2) < u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(
1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2
, 2], [0, 0], [2, 2]]]], [[2, 7, 3, 1, 1], [v = 0, And(0 < u,u < 1), And(-1 <
x,x < u^2-1), y < x-u^2+1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2
, 1/2], [-7/8, -7/8], [-2, -2], [-2, -2]]]], [[2, 7, 3, 1, 2], [v = 0, And(0 <
u,u < 1), And(-1 < x,x < u^2-1), y < x-u^2+1, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [-2, -2], [-1816187/2097152,
-3632373/4194304]]]], [[2, 7, 3, 1, 3], [v = 0, And(0 < u,u < 1), And(-1 < x,x
< u^2-1), y < x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [-2, -2], [-1/8388608, -1/
8388608]]]], [[2, 7, 3, 1, 4], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1)
, y < x-u^2+1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/8
, -7/8], [-2, -2], [908093/1048576, 454047/524288]]]], [[2, 7, 3, 1, 5], [v =
0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), y < x-u^2+1, (-u^2+1)^(1/2) < z],
[regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [-2, -2], [2, 2]]]], [[2, 
11, 7, 3, 1], [v = 0, 2^(1/2) < u, u^2-1 < x, And(u^2-x-1 < y,y < x-u^2+1), z
= z], [regular_chain, [[0, 0], [3, 3], [9, 9], [0, 0], [0, 0]]]], [[3, 11, 3,
3, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(-1 < x,x < u^2-v^
2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[1, 1], [
3299097/2097152, 3299097/2097152], [-550771/2097152, -550771/2097152], [0, 0],
[0, 0]]]], [[1, 11, 1, 2, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2))
, x < -1, y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [3299097/2097152
, 3299097/2097152], [-2, -2], [-1297479/524288, -2594957/1048576], [0, 0]]]],
[[2, 2, 5, 4, 1], [v = 0, u = -2^(1/2), 1 < x, y = x-1, z = z], [regular_chain
, [[0, 0], [-1482911/1048576, -741455/524288], [2, 2], [1, 1], [0, 0]]]], [[3,
5, 6, 4, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, y = -u^2+v^2+2, z
< -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [1, 1], [1617841/1048576, 808921/524288], [-2, -2]]]], [[3, 5, 6, 4,
2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, y = -u^2+v^2+2, z = -(-u^2+
v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576],
[1, 1], [1617841/1048576, 808921/524288], [-772605/1048576, -1545209/2097152]]
]], [[3, 5, 6, 4, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, y = -u^2+
v^2+2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [
[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [1617841/1048576, 808921
/524288], [-1/4194304, -1/4194304]]]], [[3, 5, 6, 4, 4], [0 < v, And(-(v^2+1)^
(1/2) < u,u < -v), x = 1, y = -u^2+v^2+2, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1, 1], [1617841
/1048576, 808921/524288], [193151/262144, 772605/1048576]]]], [[3, 5, 6, 4, 5]
, [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = 1, y = -u^2+v^2+2, (-u^2+v^2+1)^
(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [1,
1], [1617841/1048576, 808921/524288], [2, 2]]]], [[3, 10, 6, 1, 1], [0 < v, u
= (v^2+1)^(1/2), x = 1, y < -1, z < 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [1, 1], [-2, -2], [-1, -1]]]], [[3, 10, 6, 1, 2], [0
< v, u = (v^2+1)^(1/2), x = 1, y < -1, z = 0], [regular_chain, [[1, 1], [
741455/524288, 1482911/1048576], [1, 1], [-2, -2], [0, 0]]]], [[3, 10, 6, 1, 3
], [0 < v, u = (v^2+1)^(1/2), x = 1, y < -1, 0 < z], [regular_chain, [[1, 1],
[741455/524288, 1482911/1048576], [1, 1], [-2, -2], [1, 1]]]], [[1, 1, 2, 5, 1
], [v < 0, u < -(v^2+2)^(1/2), x = -1, u^2-v^2 < y, z = z], [regular_chain, [[
-1, -1], [-3, -3], [-1, -1], [9, 9], [0, 0]]]], [[1, 5, 7, 2, 1], [v < 0, And(
-(v^2+1)^(1/2) < u,u < v), 1 < x, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [-\
5332835/2097152, -2666417/1048576], [-2, -2]]]], [[1, 5, 7, 2, 2], [v < 0, And
(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [-\
5332835/2097152, -2666417/1048576], [-772605/1048576, -1545209/2097152]]]], [[
1, 5, 7, 2, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = u^2-v^2-x-1,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [-1265743/1048576, -1265743/1048576], [2, 2], [-5332835/2097152, -2666417/
1048576], [-1/4194304, -1/4194304]]]], [[1, 5, 7, 2, 4], [v < 0, And(-(v^2+1)^
(1/2) < u,u < v), 1 < x, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [2, 2], [-\
5332835/2097152, -2666417/1048576], [193151/262144, 772605/1048576]]]], [[1, 5
, 7, 2, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 1 < x, y = u^2-v^2-x-1, (-u
^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [2, 2], [-5332835/2097152, -2666417/1048576], [2, 2]]]], [[2, 7, 3,
2, 1], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), y = x-u^2+1, z < -(-u^
2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [-1/8, -1/8],
[-2, -2]]]], [[2, 7, 3, 2, 2], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1)
, y = x-u^2+1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/
8, -7/8], [-1/8, -1/8], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 3, 2,
3], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), y = x-u^2+1, And(-(-u^2+1
)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [-7/8,
-7/8], [-1/8, -1/8], [-1/8388608, -1/8388608]]]], [[2, 7, 3, 2, 4], [v = 0, 
And(0 < u,u < 1), And(-1 < x,x < u^2-1), y = x-u^2+1, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [-1/8, -1/8], [908093/
1048576, 454047/524288]]]], [[2, 7, 3, 2, 5], [v = 0, And(0 < u,u < 1), And(-1
< x,x < u^2-1), y = x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/
2, 1/2], [-7/8, -7/8], [-1/8, -1/8], [2, 2]]]], [[2, 11, 7, 4, 1], [v = 0, 2^(
1/2) < u, u^2-1 < x, y = x-u^2+1, z = z], [regular_chain, [[0, 0], [3, 3], [9,
9], [1, 1], [0, 0]]]], [[3, 11, 3, 2, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v
^2+2)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [-550771/2097152,
-550771/2097152], [-1546383/2097152, -773191/1048576], [0, 0]]]], [[1, 1, 3, 3
, 1], [v < 0, u < -(v^2+2)^(1/2), And(-1 < x,x < 1), And(x-u^2+v^2+1 < y,y < u
^2-v^2-x-1), z = z], [regular_chain, [[-1, -1], [-3, -3], [0, 0], [0, 0], [0,
0]]]], [[1, 6, 1, 4, 1], [v < 0, u = v, x < -1, y = -1-x, z < -1], [
regular_chain, [[-1, -1], [-1, -1], [-2, -2], [1, 1], [-2, -2]]]], [[1, 6, 1,
4, 2], [v < 0, u = v, x < -1, y = -1-x, z = -1], [regular_chain, [[-1, -1], [-\
1, -1], [-2, -2], [1, 1], [-1, -1]]]], [[1, 6, 1, 4, 3], [v < 0, u = v, x < -1
, y = -1-x, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [-2, -2],
[1, 1], [0, 0]]]], [[1, 6, 1, 4, 4], [v < 0, u = v, x < -1, y = -1-x, z = 1],
[regular_chain, [[-1, -1], [-1, -1], [-2, -2], [1, 1], [1, 1]]]], [[1, 6, 1, 4
, 5], [v < 0, u = v, x < -1, y = -1-x, 1 < z], [regular_chain, [[-1, -1], [-1,
-1], [-2, -2], [1, 1], [2, 2]]]], [[2, 7, 3, 3, 1], [v = 0, And(0 < u,u < 1),
And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [0, 0], [-2, -2]]]], [[2, 7,
3, 3, 2], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y <
u^2-x-1), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7
/8], [0, 0], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 3, 3, 3], [v = 0
, And(0 < u,u < 1), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), And(-
(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2],
[-7/8, -7/8], [0, 0], [-1/8388608, -1/8388608]]]], [[2, 7, 3, 3, 4], [v = 0, 
And(0 < u,u < 1), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), z = (-u
^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [0, 0], [
908093/1048576, 454047/524288]]]], [[2, 7, 3, 3, 5], [v = 0, And(0 < u,u < 1),
And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [0, 0], [2, 2]]]], [[3, 1, 1
, 4, 1], [0 < v, u < -(v^2+2)^(1/2), x < -1, y = u^2-v^2-x-1, z = z], [
regular_chain, [[1, 1], [-3, -3], [-2, -2], [9, 9], [0, 0]]]], [[3, 11, 3, 5,
1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(-1 < x,x < u^2-v^2-1
), u^2-v^2-x-1 < y, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097
/2097152], [-550771/2097152, -550771/2097152], [2, 2], [0, 0]]]], [[1, 10, 7,
2, 1], [v < 0, u = (v^2+1)^(1/2), 1 < x, y = -x, z < 0], [regular_chain, [[-1,
-1], [741455/524288, 1482911/1048576], [2, 2], [-2, -2], [-1, -1]]]], [[1, 10,
7, 2, 2], [v < 0, u = (v^2+1)^(1/2), 1 < x, y = -x, z = 0], [regular_chain, [[
-1, -1], [741455/524288, 1482911/1048576], [2, 2], [-2, -2], [0, 0]]]], [[1, 
10, 7, 2, 3], [v < 0, u = (v^2+1)^(1/2), 1 < x, y = -x, 0 < z], [regular_chain
, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [-2, -2], [1, 1]]]], [[
2, 2, 5, 3, 1], [v = 0, u = -2^(1/2), 1 < x, And(1-x < y,y < x-1), z = z], [
regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [2, 2], [0, 0], [0
, 0]]]], [[3, 5, 5, 2, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2
-1 < x,x < 1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-\
808921/1048576, -3235683/4194304], [-2, -2]]]], [[3, 5, 5, 2, 2], [0 < v, And(
-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304
], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 5, 2, 3], [0 < v, And(-(v^2
+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, And(-(-u^2+v
^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-808921/1048576
, -3235683/4194304], [-1/4194304, -1/4194304]]]], [[3, 5, 5, 2, 4], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304
], [193151/262144, 772605/1048576]]]], [[3, 5, 5, 2, 5], [0 < v, And(-(v^2+1)^
(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/
2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304], [2, 2]]]
], [[3, 10, 5, 3, 1], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,
y < x), z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1/
2, 1/2], [0, 0], [-1, -1]]]], [[3, 10, 5, 3, 2], [0 < v, u = (v^2+1)^(1/2), 
And(0 < x,x < 1), And(-x < y,y < x), z = 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [1/2, 1/2], [0, 0], [0, 0]]]], [[3, 10, 5, 3, 3], [0
< v, u = (v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y < x), 0 < z], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1/2, 1/2], [0, 0],
[1, 1]]]], [[1, 1, 3, 2, 1], [v < 0, u < -(v^2+2)^(1/2), And(-1 < x,x < 1), y
= x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [-3, -3], [0, 0], [-7, -7],
[0, 0]]]], [[1, 6, 1, 3, 1], [v < 0, u = v, x < -1, And(x+1 < y,y < -1-x), z <
-1], [regular_chain, [[-1, -1], [-1, -1], [-2, -2], [0, 0], [-2, -2]]]], [[1,
6, 1, 3, 2], [v < 0, u = v, x < -1, And(x+1 < y,y < -1-x), z = -1], [
regular_chain, [[-1, -1], [-1, -1], [-2, -2], [0, 0], [-1, -1]]]], [[1, 6, 1,
3, 3], [v < 0, u = v, x < -1, And(x+1 < y,y < -1-x), And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [-2, -2], [0, 0], [0, 0]]]], [[1, 6, 1, 3,
4], [v < 0, u = v, x < -1, And(x+1 < y,y < -1-x), z = 1], [regular_chain, [[-1
, -1], [-1, -1], [-2, -2], [0, 0], [1, 1]]]], [[1, 6, 1, 3, 5], [v < 0, u = v,
x < -1, And(x+1 < y,y < -1-x), 1 < z], [regular_chain, [[-1, -1], [-1, -1], [-\
2, -2], [0, 0], [2, 2]]]], [[2, 7, 3, 4, 1], [v = 0, And(0 < u,u < 1), And(-1
< x,x < u^2-1), y = u^2-x-1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1
/2, 1/2], [-7/8, -7/8], [1/8, 1/8], [-2, -2]]]], [[2, 7, 3, 4, 2], [v = 0, And
(0 < u,u < 1), And(-1 < x,x < u^2-1), y = u^2-x-1, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [1/8, 1/8], [-1816187/
2097152, -3632373/4194304]]]], [[2, 7, 3, 4, 3], [v = 0, And(0 < u,u < 1), And
(-1 < x,x < u^2-1), y = u^2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))],
[regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [1/8, 1/8], [-1/8388608, -1
/8388608]]]], [[2, 7, 3, 4, 4], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1
), y = u^2-x-1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/
8, -7/8], [1/8, 1/8], [908093/1048576, 454047/524288]]]], [[2, 7, 3, 4, 5], [v
= 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), y = u^2-x-1, (-u^2+1)^(1/2) < z]
, [regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [1/8, 1/8], [2, 2]]]], [[
3, 1, 1, 5, 1], [0 < v, u < -(v^2+2)^(1/2), x < -1, u^2-v^2-x-1 < y, z = z], [
regular_chain, [[1, 1], [-3, -3], [-2, -2], [10, 10], [0, 0]]]], [[3, 11, 3, 4
, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(-1 < x,x < u^2-v^2
-1), y = u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3299097/2097152, 
3299097/2097152], [-550771/2097152, -550771/2097152], [773191/1048576, 96649/
131072], [0, 0]]]], [[1, 10, 7, 1, 1], [v < 0, u = (v^2+1)^(1/2), 1 < x, y < -
x, z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2]
, [-3, -3], [-1, -1]]]], [[1, 10, 7, 1, 2], [v < 0, u = (v^2+1)^(1/2), 1 < x,
y < -x, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [
2, 2], [-3, -3], [0, 0]]]], [[1, 10, 7, 1, 3], [v < 0, u = (v^2+1)^(1/2), 1 <
x, y < -x, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576]
, [2, 2], [-3, -3], [1, 1]]]], [[2, 2, 5, 2, 1], [v = 0, u = -2^(1/2), 1 < x,
y = 1-x, z = z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288],
[2, 2], [-1, -1], [0, 0]]]], [[3, 5, 5, 3, 1], [0 < v, And(-(v^2+1)^(1/2) < u,
u < -v), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -
(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [-2, -2]
]]], [[3, 5, 5, 3, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 <
x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152,
479311/2097152], [-3/8388608, -3/8388608], [-772605/1048576, -1545209/2097152]
]]], [[3, 5, 5, 3, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 <
x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z
< (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [-1/
4194304, -1/4194304]]]], [[3, 5, 5, 3, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u <
-v), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2
+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576],
[479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [193151/262144, 
772605/1048576]]]], [[3, 5, 5, 3, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(
1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [2, 2]]]], [[3, 10,
5, 4, 1], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1), y = x, z < 0], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1/2, 1/2], [1/2, 1/
2], [-1, -1]]]], [[3, 10, 5, 4, 2], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1
), y = x, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [
1/2, 1/2], [1/2, 1/2], [0, 0]]]], [[3, 10, 5, 4, 3], [0 < v, u = (v^2+1)^(1/2)
, And(0 < x,x < 1), y = x, 0 < z], [regular_chain, [[1, 1], [741455/524288, 
1482911/1048576], [1/2, 1/2], [1/2, 1/2], [1, 1]]]], [[1, 1, 3, 5, 1], [v < 0,
u < -(v^2+2)^(1/2), And(-1 < x,x < 1), u^2-v^2-x-1 < y, z = z], [regular_chain
, [[-1, -1], [-3, -3], [0, 0], [8, 8], [0, 0]]]], [[1, 6, 1, 2, 1], [v < 0, u
= v, x < -1, y = x+1, z < -1], [regular_chain, [[-1, -1], [-1, -1], [-2, -2],
[-1, -1], [-2, -2]]]], [[1, 6, 1, 2, 2], [v < 0, u = v, x < -1, y = x+1, z = -\
1], [regular_chain, [[-1, -1], [-1, -1], [-2, -2], [-1, -1], [-1, -1]]]], [[1,
6, 1, 2, 3], [v < 0, u = v, x < -1, y = x+1, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [-2, -2], [-1, -1], [0, 0]]]], [[1, 6, 1,
2, 4], [v < 0, u = v, x < -1, y = x+1, z = 1], [regular_chain, [[-1, -1], [-1,
-1], [-2, -2], [-1, -1], [1, 1]]]], [[1, 6, 1, 2, 5], [v < 0, u = v, x < -1, y
= x+1, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [-2, -2], [-1, -1], [2, 2]
]]], [[2, 7, 3, 5, 1], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), u^2-x-\
1 < y, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8]
, [2, 2], [-2, -2]]]], [[2, 7, 3, 5, 2], [v = 0, And(0 < u,u < 1), And(-1 < x,
x < u^2-1), u^2-x-1 < y, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2,
1/2], [-7/8, -7/8], [2, 2], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 3
, 5, 3], [v = 0, And(0 < u,u < 1), And(-1 < x,x < u^2-1), u^2-x-1 < y, And(-(-
u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [-\
7/8, -7/8], [2, 2], [-1/8388608, -1/8388608]]]], [[2, 7, 3, 5, 4], [v = 0, And
(0 < u,u < 1), And(-1 < x,x < u^2-1), u^2-x-1 < y, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-7/8, -7/8], [2, 2], [908093/1048576, 
454047/524288]]]], [[2, 7, 3, 5, 5], [v = 0, And(0 < u,u < 1), And(-1 < x,x <
u^2-1), u^2-x-1 < y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2],
[-7/8, -7/8], [2, 2], [2, 2]]]], [[3, 1, 1, 2, 1], [0 < v, u < -(v^2+2)^(1/2),
x < -1, y = x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-3, -3], [-2, -2],
[-9, -9], [0, 0]]]], [[3, 11, 4, 2, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2
+2)^(1/2)), x = u^2-v^2-1, y = 0, z = z], [regular_chain, [[1, 1], [3299097/
2097152, 3299097/2097152], [497805/1048576, 248903/524288], [0, 0], [0, 0]]]],
[[1, 10, 7, 4, 1], [v < 0, u = (v^2+1)^(1/2), 1 < x, y = x, z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [2, 2], [-\
1, -1]]]], [[1, 10, 7, 4, 2], [v < 0, u = (v^2+1)^(1/2), 1 < x, y = x, z = 0],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [2, 2], [
0, 0]]]], [[1, 10, 7, 4, 3], [v < 0, u = (v^2+1)^(1/2), 1 < x, y = x, 0 < z],
[regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [2, 2], [
1, 1]]]], [[2, 2, 5, 1, 1], [v = 0, u = -2^(1/2), 1 < x, y < 1-x, z = z], [
regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [2, 2], [-2, -2],
[0, 0]]]], [[3, 5, 5, 4, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v
^2-1 < x,x < 1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152],
[101115/131072, 808921/1048576], [-2, -2]]]], [[3, 5, 5, 4, 2], [0 < v, And(-(
v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z = -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576]
, [479311/2097152, 479311/2097152], [101115/131072, 808921/1048576], [-772605/
1048576, -1545209/2097152]]]], [[3, 5, 5, 4, 3], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [479311/2097152, 479311/2097152], [101115/131072, 808921/
1048576], [-1/4194304, -1/4194304]]]], [[3, 5, 5, 4, 4], [0 < v, And(-(v^2+1)^
(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
479311/2097152, 479311/2097152], [101115/131072, 808921/1048576], [193151/
262144, 772605/1048576]]]], [[3, 5, 5, 4, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u
< -v), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152,
479311/2097152], [101115/131072, 808921/1048576], [2, 2]]]], [[3, 10, 5, 1, 1]
, [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1), y < -x, z < 0], [regular_chain,
[[1, 1], [741455/524288, 1482911/1048576], [1/2, 1/2], [-2, -2], [-1, -1]]]],
[[3, 10, 5, 1, 2], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1), y < -x, z = 0]
, [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1/2, 1/2], [-2,
-2], [0, 0]]]], [[3, 10, 5, 1, 3], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1)
, y < -x, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [
1/2, 1/2], [-2, -2], [1, 1]]]], [[1, 1, 3, 4, 1], [v < 0, u < -(v^2+2)^(1/2),
And(-1 < x,x < 1), y = u^2-v^2-x-1, z = z], [regular_chain, [[-1, -1], [-3, -3
], [0, 0], [7, 7], [0, 0]]]], [[1, 6, 1, 1, 1], [v < 0, u = v, x < -1, y < x+1
, z < -1], [regular_chain, [[-1, -1], [-1, -1], [-2, -2], [-2, -2], [-2, -2]]]
], [[1, 6, 1, 1, 2], [v < 0, u = v, x < -1, y < x+1, z = -1], [regular_chain,
[[-1, -1], [-1, -1], [-2, -2], [-2, -2], [-1, -1]]]], [[1, 6, 1, 1, 3], [v < 0
, u = v, x < -1, y < x+1, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1,
-1], [-2, -2], [-2, -2], [0, 0]]]], [[1, 6, 1, 1, 4], [v < 0, u = v, x < -1, y
< x+1, z = 1], [regular_chain, [[-1, -1], [-1, -1], [-2, -2], [-2, -2], [1, 1]
]]], [[1, 6, 1, 1, 5], [v < 0, u = v, x < -1, y < x+1, 1 < z], [regular_chain,
[[-1, -1], [-1, -1], [-2, -2], [-2, -2], [2, 2]]]], [[2, 7, 4, 1, 1], [v = 0,
And(0 < u,u < 1), x = u^2-1, y < 0, z < -(-u^2+1)^(1/2)], [regular_chain, [[0,
0], [1/2, 1/2], [-3/4, -3/4], [-1, -1], [-2, -2]]]], [[2, 7, 4, 1, 2], [v = 0,
And(0 < u,u < 1), x = u^2-1, y < 0, z = -(-u^2+1)^(1/2)], [regular_chain, [[0,
0], [1/2, 1/2], [-3/4, -3/4], [-1, -1], [-1816187/2097152, -3632373/4194304]]]
], [[2, 7, 4, 1, 3], [v = 0, And(0 < u,u < 1), x = u^2-1, y < 0, And(-(-u^2+1)
^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -\
3/4], [-1, -1], [-1/8388608, -1/8388608]]]], [[2, 7, 4, 1, 4], [v = 0, And(0 <
u,u < 1), x = u^2-1, y < 0, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2
, 1/2], [-3/4, -3/4], [-1, -1], [908093/1048576, 454047/524288]]]], [[2, 7, 4,
1, 5], [v = 0, And(0 < u,u < 1), x = u^2-1, y < 0, (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [1/2, 1/2], [-3/4, -3/4], [-1, -1], [2, 2]]]], [[3, 1,
1, 3, 1], [0 < v, u < -(v^2+2)^(1/2), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-
x-1), z = z], [regular_chain, [[1, 1], [-3, -3], [-2, -2], [0, 0], [0, 0]]]],
[[3, 11, 4, 1, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = u^2-v
^2-1, y < 0, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/
2097152], [497805/1048576, 248903/524288], [-1, -1], [0, 0]]]], [[1, 10, 7, 3,
1], [v < 0, u = (v^2+1)^(1/2), 1 < x, And(-x < y,y < x), z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2], [0, 0], [-\
1, -1]]]], [[1, 10, 7, 3, 2], [v < 0, u = (v^2+1)^(1/2), 1 < x, And(-x < y,y <
x), z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [2, 2
], [0, 0], [0, 0]]]], [[1, 10, 7, 3, 3], [v < 0, u = (v^2+1)^(1/2), 1 < x, And
(-x < y,y < x), 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [2, 2], [0, 0], [1, 1]]]], [[2, 2, 4, 3, 1], [v = 0, u = -2^(1/2), x
= 1, 0 < y, z = z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288
], [1, 1], [1, 1], [0, 0]]]], [[3, 5, 5, 5, 1], [0 < v, And(-(v^2+1)^(1/2) < u
,u < -v), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152
, 479311/2097152], [2, 2], [-2, -2]]]], [[3, 5, 5, 5, 2], [0 < v, And(-(v^2+1)
^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
479311/2097152, 479311/2097152], [2, 2], [-772605/1048576, -1545209/2097152]]]
], [[3, 5, 5, 5, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x
,x < 1), x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))]
, [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [2, 2], [-1/4194304, -1/4194304]]]], [[3, 5, 5, 5, 4
], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2
+1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [479311/2097152, 479311/2097152], [2, 2], [193151/262144, 
772605/1048576]]]], [[3, 5, 5, 5, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152,
479311/2097152], [2, 2], [2, 2]]]], [[3, 10, 5, 2, 1], [0 < v, u = (v^2+1)^(1/
2), And(0 < x,x < 1), y = -x, z < 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [1/2, 1/2], [-1/2, -1/2], [-1, -1]]]], [[3, 10, 5, 2, 2], [0
< v, u = (v^2+1)^(1/2), And(0 < x,x < 1), y = -x, z = 0], [regular_chain, [[1,
1], [741455/524288, 1482911/1048576], [1/2, 1/2], [-1/2, -1/2], [0, 0]]]], [[3
, 10, 5, 2, 3], [0 < v, u = (v^2+1)^(1/2), And(0 < x,x < 1), y = -x, 0 < z], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [1/2, 1/2], [-1/2, -\
1/2], [1, 1]]]], [[1, 11, 2, 5, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^
(1/2)), x = -1, u^2-v^2 < y, z = z], [regular_chain, [[-1, -1], [3299097/
2097152, 3299097/2097152], [-1, -1], [3, 3], [0, 0]]]], [[2, 1, 7, 3, 1], [v =
0, u < -2^(1/2), u^2-1 < x, And(u^2-x-1 < y,y < x-u^2+1), z = z], [
regular_chain, [[0, 0], [-3, -3], [9, 9], [0, 0], [0, 0]]]], [[3, 6, 4, 5, 1],
[0 < v, u = -v, x = 1, 2 < y, z < -1], [regular_chain, [[1, 1], [-1, -1], [1,
1], [3, 3], [-2, -2]]]], [[3, 6, 4, 5, 2], [0 < v, u = -v, x = 1, 2 < y, z = -\
1], [regular_chain, [[1, 1], [-1, -1], [1, 1], [3, 3], [-1, -1]]]], [[3, 6, 4,
5, 3], [0 < v, u = -v, x = 1, 2 < y, And(-1 < z,z < 1)], [regular_chain, [[1,
1], [-1, -1], [1, 1], [3, 3], [0, 0]]]], [[3, 6, 4, 5, 4], [0 < v, u = -v, x =
1, 2 < y, z = 1], [regular_chain, [[1, 1], [-1, -1], [1, 1], [3, 3], [1, 1]]]]
, [[3, 6, 4, 5, 5], [0 < v, u = -v, x = 1, 2 < y, 1 < z], [regular_chain, [[1,
1], [-1, -1], [1, 1], [3, 3], [2, 2]]]], [[3, 10, 4, 1, 1], [0 < v, u = (v^2+1
)^(1/2), x = 0, y < 0, z < 0], [regular_chain, [[1, 1], [741455/524288, 
1482911/1048576], [0, 0], [-1, -1], [-1, -1]]]], [[3, 10, 4, 1, 2], [0 < v, u
= (v^2+1)^(1/2), x = 0, y < 0, z = 0], [regular_chain, [[1, 1], [741455/524288
, 1482911/1048576], [0, 0], [-1, -1], [0, 0]]]], [[3, 10, 4, 1, 3], [0 < v, u
= (v^2+1)^(1/2), x = 0, y < 0, 0 < z], [regular_chain, [[1, 1], [741455/524288
, 1482911/1048576], [0, 0], [-1, -1], [1, 1]]]], [[1, 1, 4, 3, 1], [v < 0, u <
-(v^2+2)^(1/2), x = 1, And(-u^2+v^2+2 < y,y < u^2-v^2-2), z = z], [
regular_chain, [[-1, -1], [-3, -3], [1, 1], [0, 0], [0, 0]]]], [[1, 5, 2, 1, 1
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, y < -u^2+v^2, z < -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [
-1, -1], [-2, -2], [-2, -2]]]], [[1, 5, 2, 1, 2], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = -1, y < -u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1
, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-2, -2], [-772605/
1048576, -1545209/2097152]]]], [[1, 5, 2, 1, 3], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = -1, y < -u^2+v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(
1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1,
-1], [-2, -2], [-1/4194304, -1/4194304]]]], [[1, 5, 2, 1, 4], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x = -1, y < -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-2,
-2], [193151/262144, 772605/1048576]]]], [[1, 5, 2, 1, 5], [v < 0, And(-(v^2+1
)^(1/2) < u,u < v), x = -1, y < -u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-2,
-2], [2, 2]]]], [[2, 8, 1, 3, 1], [v = 0, u = 1, x < -1, And(x < y,y < -x), z
< 0], [regular_chain, [[0, 0], [1, 1], [-2, -2], [0, 0], [-1, -1]]]], [[2, 8,
1, 3, 2], [v = 0, u = 1, x < -1, And(x < y,y < -x), z = 0], [regular_chain, [[
0, 0], [1, 1], [-2, -2], [0, 0], [0, 0]]]], [[2, 8, 1, 3, 3], [v = 0, u = 1, x
< -1, And(x < y,y < -x), 0 < z], [regular_chain, [[0, 0], [1, 1], [-2, -2], [0
, 0], [1, 1]]]], [[2, 11, 5, 4, 1], [v = 0, 2^(1/2) < u, And(1 < x,x < u^2-1),
y = u^2-x-1, z = z], [regular_chain, [[0, 0], [3, 3], [9/2, 9/2], [7/2, 7/2],
[0, 0]]]], [[3, 11, 5, 2, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2))
, And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = z], [regular_chain, [[1, 1],
[3299097/2097152, 3299097/2097152], [773191/1048576, 773191/1048576], [-137693
/524288, -275385/1048576], [0, 0]]]], [[1, 11, 3, 1, 1], [v < 0, And((v^2+1)^(
1/2) < u,u < (v^2+2)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = z
], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [-550771/
2097152, -550771/2097152], [-2, -2], [0, 0]]]], [[2, 1, 7, 4, 1], [v = 0, u <
-2^(1/2), u^2-1 < x, y = x-u^2+1, z = z], [regular_chain, [[0, 0], [-3, -3], [
9, 9], [1, 1], [0, 0]]]], [[3, 6, 4, 4, 1], [0 < v, u = -v, x = 1, y = 2, z <
-1], [regular_chain, [[1, 1], [-1, -1], [1, 1], [2, 2], [-2, -2]]]], [[3, 6, 4
, 4, 2], [0 < v, u = -v, x = 1, y = 2, z = -1], [regular_chain, [[1, 1], [-1,
-1], [1, 1], [2, 2], [-1, -1]]]], [[3, 6, 4, 4, 3], [0 < v, u = -v, x = 1, y =
2, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [1, 1], [2, 2], [0,
0]]]], [[3, 6, 4, 4, 4], [0 < v, u = -v, x = 1, y = 2, z = 1], [regular_chain,
[[1, 1], [-1, -1], [1, 1], [2, 2], [1, 1]]]], [[3, 6, 4, 4, 5], [0 < v, u = -v
, x = 1, y = 2, 1 < z], [regular_chain, [[1, 1], [-1, -1], [1, 1], [2, 2], [2,
2]]]], [[3, 10, 3, 5, 1], [0 < v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), -x < y
, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1/2, -1
/2], [2, 2], [-1, -1]]]], [[3, 10, 3, 5, 2], [0 < v, u = (v^2+1)^(1/2), And(-1
< x,x < 0), -x < y, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [-1/2, -1/2], [2, 2], [0, 0]]]], [[3, 10, 3, 5, 3], [0 < v, u = (v^2
+1)^(1/2), And(-1 < x,x < 0), -x < y, 0 < z], [regular_chain, [[1, 1], [741455
/524288, 1482911/1048576], [-1/2, -1/2], [2, 2], [1, 1]]]], [[1, 1, 4, 4, 1],
[v < 0, u < -(v^2+2)^(1/2), x = 1, y = u^2-v^2-2, z = z], [regular_chain, [[-1
, -1], [-3, -3], [1, 1], [6, 6], [0, 0]]]], [[1, 5, 2, 2, 1], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x = -1, y = -u^2+v^2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [-2, -2]]]], [[1, 5, 2, 2, 2], [v < 0, And(-(
v^2+1)^(1/2) < u,u < v), x = -1, y = -u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [-772605/1048576, -1545209/2097152]]]], [[1,
5, 2, 2, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, y = -u^2+v^2, And(
-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
-1265743/1048576, -1265743/1048576], [-1, -1], [-479311/1048576, -239655/
524288], [-1/4194304, -1/4194304]]]], [[1, 5, 2, 2, 4], [v < 0, And(-(v^2+1)^(
1/2) < u,u < v), x = -1, y = -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain
, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-479311/1048576,
-239655/524288], [193151/262144, 772605/1048576]]]], [[1, 5, 2, 2, 5], [v < 0,
And(-(v^2+1)^(1/2) < u,u < v), x = -1, y = -u^2+v^2, (-u^2+v^2+1)^(1/2) < z],
[regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [2, 2]]]], [[2, 8, 1, 2, 1], [v = 0, u = 1, x
< -1, y = x, z < 0], [regular_chain, [[0, 0], [1, 1], [-2, -2], [-2, -2], [-1,
-1]]]], [[2, 8, 1, 2, 2], [v = 0, u = 1, x < -1, y = x, z = 0], [regular_chain
, [[0, 0], [1, 1], [-2, -2], [-2, -2], [0, 0]]]], [[2, 8, 1, 2, 3], [v = 0, u
= 1, x < -1, y = x, 0 < z], [regular_chain, [[0, 0], [1, 1], [-2, -2], [-2, -2
], [1, 1]]]], [[2, 11, 5, 3, 1], [v = 0, 2^(1/2) < u, And(1 < x,x < u^2-1), 
And(x-u^2+1 < y,y < u^2-x-1), z = z], [regular_chain, [[0, 0], [3, 3], [9/2, 9
/2], [0, 0], [0, 0]]]], [[3, 11, 5, 3, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (
v^2+2)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1),
z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [773191/
1048576, 773191/1048576], [0, 0], [0, 0]]]], [[1, 11, 2, 3, 1], [v < 0, And((v
^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z =
z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [-1, -1], [
0, 0], [0, 0]]]], [[2, 1, 7, 5, 1], [v = 0, u < -2^(1/2), u^2-1 < x, x-u^2+1 <
y, z = z], [regular_chain, [[0, 0], [-3, -3], [9, 9], [2, 2], [0, 0]]]], [[3,
6, 4, 3, 1], [0 < v, u = -v, x = 1, And(-2 < y,y < 2), z < -1], [regular_chain
, [[1, 1], [-1, -1], [1, 1], [0, 0], [-2, -2]]]], [[3, 6, 4, 3, 2], [0 < v, u
= -v, x = 1, And(-2 < y,y < 2), z = -1], [regular_chain, [[1, 1], [-1, -1], [1
, 1], [0, 0], [-1, -1]]]], [[3, 6, 4, 3, 3], [0 < v, u = -v, x = 1, And(-2 < y
,y < 2), And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [1, 1], [0, 0]
, [0, 0]]]], [[3, 6, 4, 3, 4], [0 < v, u = -v, x = 1, And(-2 < y,y < 2), z = 1
], [regular_chain, [[1, 1], [-1, -1], [1, 1], [0, 0], [1, 1]]]], [[3, 6, 4, 3,
5], [0 < v, u = -v, x = 1, And(-2 < y,y < 2), 1 < z], [regular_chain, [[1, 1],
[-1, -1], [1, 1], [0, 0], [2, 2]]]], [[3, 10, 4, 3, 1], [0 < v, u = (v^2+1)^(1
/2), x = 0, 0 < y, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [0, 0], [1, 1], [-1, -1]]]], [[3, 10, 4, 3, 2], [0 < v, u = (v^2+1)^
(1/2), x = 0, 0 < y, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [0, 0], [1, 1], [0, 0]]]], [[3, 10, 4, 3, 3], [0 < v, u = (v^2+1)^(1
/2), x = 0, 0 < y, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [0, 0], [1, 1], [1, 1]]]], [[1, 1, 4, 1, 1], [v < 0, u < -(v^2+2)^(1
/2), x = 1, y < -u^2+v^2+2, z = z], [regular_chain, [[-1, -1], [-3, -3], [1, 1
], [-7, -7], [0, 0]]]], [[1, 5, 2, 3, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v
), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [0,
0], [-2, -2]]]], [[1, 5, 2, 3, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x =
-1, And(-u^2+v^2 < y,y < u^2-v^2), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [0, 0], [-772605/
1048576, -1545209/2097152]]]], [[1, 5, 2, 3, 3], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), And(-(-u^2+v^2+1)^(1/2) < z,z
< (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743
/1048576], [-1, -1], [0, 0], [-1/4194304, -1/4194304]]]], [[1, 5, 2, 3, 4], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-1, -1], [0, 0], [193151/262144, 772605/1048576]]]], [[1, 5, 2, 3,
5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, And(-u^2+v^2 < y,y < u^2-v^
2), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-1, -1], [0, 0], [2, 2]]]], [[2, 8, 1, 1, 1], [v = 0, u = 1
, x < -1, y < x, z < 0], [regular_chain, [[0, 0], [1, 1], [-2, -2], [-3, -3],
[-1, -1]]]], [[2, 8, 1, 1, 2], [v = 0, u = 1, x < -1, y < x, z = 0], [
regular_chain, [[0, 0], [1, 1], [-2, -2], [-3, -3], [0, 0]]]], [[2, 8, 1, 1, 3
], [v = 0, u = 1, x < -1, y < x, 0 < z], [regular_chain, [[0, 0], [1, 1], [-2,
-2], [-3, -3], [1, 1]]]], [[2, 11, 6, 1, 1], [v = 0, 2^(1/2) < u, x = u^2-1, y
< 0, z = z], [regular_chain, [[0, 0], [3, 3], [8, 8], [-1, -1], [0, 0]]]], [[3
, 11, 4, 3, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = u^2-v^2-\
1, 0 < y, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152],
[497805/1048576, 248903/524288], [1, 1], [0, 0]]]], [[1, 11, 2, 4, 1], [v < 0,
And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -1, y = u^2-v^2, z = z], [
regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [-1, -1], [
1546381/1048576, 773191/524288], [0, 0]]]], [[2, 2, 1, 1, 1], [v = 0, u = -2^(
1/2), x < -1, y < x-1, z = z], [regular_chain, [[0, 0], [-1482911/1048576, -\
741455/524288], [-2, -2], [-4, -4], [0, 0]]]], [[3, 6, 4, 2, 1], [0 < v, u = -
v, x = 1, y = -2, z < -1], [regular_chain, [[1, 1], [-1, -1], [1, 1], [-2, -2]
, [-2, -2]]]], [[3, 6, 4, 2, 2], [0 < v, u = -v, x = 1, y = -2, z = -1], [
regular_chain, [[1, 1], [-1, -1], [1, 1], [-2, -2], [-1, -1]]]], [[3, 6, 4, 2,
3], [0 < v, u = -v, x = 1, y = -2, And(-1 < z,z < 1)], [regular_chain, [[1, 1]
, [-1, -1], [1, 1], [-2, -2], [0, 0]]]], [[3, 6, 4, 2, 4], [0 < v, u = -v, x =
1, y = -2, z = 1], [regular_chain, [[1, 1], [-1, -1], [1, 1], [-2, -2], [1, 1]
]]], [[3, 6, 4, 2, 5], [0 < v, u = -v, x = 1, y = -2, 1 < z], [regular_chain,
[[1, 1], [-1, -1], [1, 1], [-2, -2], [2, 2]]]], [[3, 10, 4, 2, 1], [0 < v, u =
(v^2+1)^(1/2), x = 0, y = 0, z < 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [0, 0], [0, 0], [-1, -1]]]], [[3, 10, 4, 2, 2], [0 < v, u =
(v^2+1)^(1/2), x = 0, y = 0, z = 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [0, 0], [0, 0], [0, 0]]]], [[3, 10, 4, 2, 3], [0 < v, u = (v
^2+1)^(1/2), x = 0, y = 0, 0 < z], [regular_chain, [[1, 1], [741455/524288, 
1482911/1048576], [0, 0], [0, 0], [1, 1]]]], [[1, 1, 4, 2, 1], [v < 0, u < -(v
^2+2)^(1/2), x = 1, y = -u^2+v^2+2, z = z], [regular_chain, [[-1, -1], [-3, -3
], [1, 1], [-6, -6], [0, 0]]]], [[1, 5, 2, 4, 1], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), x = -1, y = u^2-v^2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [-1265743/1048576, -1265743/1048576], [-1, -1], [239655/524288, 479311/
1048576], [-2, -2]]]], [[1, 5, 2, 4, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v)
, x = -1, y = u^2-v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [-1, -1], [239655/524288, 479311/1048576],
[-772605/1048576, -1545209/2097152]]]], [[1, 5, 2, 4, 3], [v < 0, And(-(v^2+1)
^(1/2) < u,u < v), x = -1, y = u^2-v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+
v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576
], [-1, -1], [239655/524288, 479311/1048576], [-1/4194304, -1/4194304]]]], [[1
, 5, 2, 4, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, y = u^2-v^2, z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-1, -1], [239655/524288, 479311/1048576], [193151/262144, 772605/
1048576]]]], [[1, 5, 2, 4, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1,
y = u^2-v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [-1, -1], [239655/524288, 479311/1048576], [2, 2]]
]], [[2, 7, 7, 5, 1], [v = 0, And(0 < u,u < 1), 1 < x, x-u^2+1 < y, z < -(-u^2
+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [4, 4], [-2, -2]]]],
[[2, 7, 7, 5, 2], [v = 0, And(0 < u,u < 1), 1 < x, x-u^2+1 < y, z = -(-u^2+1)^
(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [4, 4], [-1816187/2097152
, -3632373/4194304]]]], [[2, 7, 7, 5, 3], [v = 0, And(0 < u,u < 1), 1 < x, x-u
^2+1 < y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0
], [1/2, 1/2], [2, 2], [4, 4], [-1/8388608, -1/8388608]]]], [[2, 7, 7, 5, 4],
[v = 0, And(0 < u,u < 1), 1 < x, x-u^2+1 < y, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [4, 4], [908093/1048576, 454047/
524288]]]], [[2, 7, 7, 5, 5], [v = 0, And(0 < u,u < 1), 1 < x, x-u^2+1 < y, (-
u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [4, 4], [2, 2]
]]], [[2, 11, 5, 5, 1], [v = 0, 2^(1/2) < u, And(1 < x,x < u^2-1), u^2-x-1 < y
, z = z], [regular_chain, [[0, 0], [3, 3], [9/2, 9/2], [5, 5], [0, 0]]]], [[3,
11, 5, 1, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(u^2-v^2-1
< x,x < 1), y < u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3299097/2097152
, 3299097/2097152], [773191/1048576, 773191/1048576], [-2, -2], [0, 0]]]], [[1
, 1, 5, 2, 1], [v < 0, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), y = x-u^2
+v^2+1, z = z], [regular_chain, [[-1, -1], [-3, -3], [4, 4], [-3, -3], [0, 0]]
]], [[1, 5, 2, 5, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, u^2-v^2 <
y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-1, -1], [2, 2], [-2, -2]]]], [[1, 5, 2, 5, 2], [v < 0, And
(-(v^2+1)^(1/2) < u,u < v), x = -1, u^2-v^2 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [2,
2], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 2, 5, 3], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x = -1, u^2-v^2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-
u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-1, -1], [2, 2], [-1/4194304, -1/4194304]]]], [[1, 5, 2, 5, 4], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), x = -1, u^2-v^2 < y, z = (-u^2+v^2+1)^(1/2
)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1],
[2, 2], [193151/262144, 772605/1048576]]]], [[1, 5, 2, 5, 5], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x = -1, u^2-v^2 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1, -1], [2,
2], [2, 2]]]], [[2, 8, 2, 2, 1], [v = 0, u = 1, x = -1, y = -1, z < 0], [
regular_chain, [[0, 0], [1, 1], [-1, -1], [-1, -1], [-1, -1]]]], [[2, 8, 2, 2,
2], [v = 0, u = 1, x = -1, y = -1, z = 0], [regular_chain, [[0, 0], [1, 1], [-\
1, -1], [-1, -1], [0, 0]]]], [[2, 8, 2, 2, 3], [v = 0, u = 1, x = -1, y = -1,
0 < z], [regular_chain, [[0, 0], [1, 1], [-1, -1], [-1, -1], [1, 1]]]], [[2, 
11, 6, 3, 1], [v = 0, 2^(1/2) < u, x = u^2-1, 0 < y, z = z], [regular_chain, [
[0, 0], [3, 3], [8, 8], [1, 1], [0, 0]]]], [[3, 11, 6, 1, 1], [0 < v, And((v^2
+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = 1, y < u^2-v^2-2, z = z], [regular_chain
, [[1, 1], [3299097/2097152, 3299097/2097152], [1, 1], [-2, -2], [0, 0]]]], [[
1, 11, 2, 1, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -1, y <
-u^2+v^2, z = z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152
], [-1, -1], [-3, -3], [0, 0]]]], [[2, 1, 6, 2, 1], [v = 0, u < -2^(1/2), x =
u^2-1, y = 0, z = z], [regular_chain, [[0, 0], [-3, -3], [8, 8], [0, 0], [0, 0
]]]], [[3, 6, 4, 1, 1], [0 < v, u = -v, x = 1, y < -2, z < -1], [regular_chain
, [[1, 1], [-1, -1], [1, 1], [-3, -3], [-2, -2]]]], [[3, 6, 4, 1, 2], [0 < v,
u = -v, x = 1, y < -2, z = -1], [regular_chain, [[1, 1], [-1, -1], [1, 1], [-3
, -3], [-1, -1]]]], [[3, 6, 4, 1, 3], [0 < v, u = -v, x = 1, y < -2, And(-1 <
z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [1, 1], [-3, -3], [0, 0]]]], [[3
, 6, 4, 1, 4], [0 < v, u = -v, x = 1, y < -2, z = 1], [regular_chain, [[1, 1],
[-1, -1], [1, 1], [-3, -3], [1, 1]]]], [[3, 6, 4, 1, 5], [0 < v, u = -v, x = 1
, y < -2, 1 < z], [regular_chain, [[1, 1], [-1, -1], [1, 1], [-3, -3], [2, 2]]
]], [[3, 10, 3, 2, 1], [0 < v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y = x, z
< 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1/2, -1/2],
[-1/2, -1/2], [-1, -1]]]], [[3, 10, 3, 2, 2], [0 < v, u = (v^2+1)^(1/2), And(-\
1 < x,x < 0), y = x, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [-1/2, -1/2], [-1/2, -1/2], [0, 0]]]], [[3, 10, 3, 2, 3], [0 < v, u
= (v^2+1)^(1/2), And(-1 < x,x < 0), y = x, 0 < z], [regular_chain, [[1, 1], [
741455/524288, 1482911/1048576], [-1/2, -1/2], [-1/2, -1/2], [1, 1]]]], [[1, 1
, 5, 3, 1], [v < 0, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), And(x-u^2+v^
2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[-1, -1], [-3, -3], [4, 4],
[0, 0], [0, 0]]]], [[1, 5, 3, 1, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), 
And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [-2, -2], [-2, -2]]]], [[1, 5, 3, 1, 2], [v < 0, 
And(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-772605/1048576, -\
1545209/2097152]]]], [[1, 5, 3, 1, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v),
And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-
u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-1/4194304, -1/
4194304]]]], [[1, 5, 3, 1, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(-1 <
x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/
4194304], [-2, -2], [193151/262144, 772605/1048576]]]], [[1, 5, 3, 1, 5], [v <
0, And(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1,
(-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [2, 2]]]], [
[2, 8, 2, 1, 1], [v = 0, u = 1, x = -1, y < -1, z < 0], [regular_chain, [[0, 0
], [1, 1], [-1, -1], [-2, -2], [-1, -1]]]], [[2, 8, 2, 1, 2], [v = 0, u = 1, x
= -1, y < -1, z = 0], [regular_chain, [[0, 0], [1, 1], [-1, -1], [-2, -2], [0,
0]]]], [[2, 8, 2, 1, 3], [v = 0, u = 1, x = -1, y < -1, 0 < z], [regular_chain
, [[0, 0], [1, 1], [-1, -1], [-2, -2], [1, 1]]]], [[2, 11, 6, 2, 1], [v = 0, 2
^(1/2) < u, x = u^2-1, y = 0, z = z], [regular_chain, [[0, 0], [3, 3], [8, 8],
[0, 0], [0, 0]]]], [[3, 11, 6, 2, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2
)^(1/2)), x = 1, y = u^2-v^2-2, z = z], [regular_chain, [[1, 1], [3299097/
2097152, 3299097/2097152], [1, 1], [-1101541/2097152, -275385/524288], [0, 0]]
]], [[1, 11, 2, 2, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = -\
1, y = -u^2+v^2, z = z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/
2097152], [-1, -1], [-773191/524288, -1546381/1048576], [0, 0]]]], [[2, 1, 6,
3, 1], [v = 0, u < -2^(1/2), x = u^2-1, 0 < y, z = z], [regular_chain, [[0, 0]
, [-3, -3], [8, 8], [1, 1], [0, 0]]]], [[3, 6, 3, 5, 1], [0 < v, u = -v, And(-\
1 < x,x < 1), x+1 < y, z < -1], [regular_chain, [[1, 1], [-1, -1], [0, 0], [2,
2], [-2, -2]]]], [[3, 6, 3, 5, 2], [0 < v, u = -v, And(-1 < x,x < 1), x+1 < y,
z = -1], [regular_chain, [[1, 1], [-1, -1], [0, 0], [2, 2], [-1, -1]]]], [[3,
6, 3, 5, 3], [0 < v, u = -v, And(-1 < x,x < 1), x+1 < y, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [2, 2], [0, 0]]]], [[3, 6, 3, 5, 4],
[0 < v, u = -v, And(-1 < x,x < 1), x+1 < y, z = 1], [regular_chain, [[1, 1], [
-1, -1], [0, 0], [2, 2], [1, 1]]]], [[3, 6, 3, 5, 5], [0 < v, u = -v, And(-1 <
x,x < 1), x+1 < y, 1 < z], [regular_chain, [[1, 1], [-1, -1], [0, 0], [2, 2],
[2, 2]]]], [[3, 10, 3, 1, 1], [0 < v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y
< x, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1/2,
-1/2], [-2, -2], [-1, -1]]]], [[3, 10, 3, 1, 2], [0 < v, u = (v^2+1)^(1/2), 
And(-1 < x,x < 0), y < x, z = 0], [regular_chain, [[1, 1], [741455/524288, 
1482911/1048576], [-1/2, -1/2], [-2, -2], [0, 0]]]], [[3, 10, 3, 1, 3], [0 < v
, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y < x, 0 < z], [regular_chain, [[1, 1]
, [741455/524288, 1482911/1048576], [-1/2, -1/2], [-2, -2], [1, 1]]]], [[1, 1,
4, 5, 1], [v < 0, u < -(v^2+2)^(1/2), x = 1, u^2-v^2-2 < y, z = z], [
regular_chain, [[-1, -1], [-3, -3], [1, 1], [7, 7], [0, 0]]]], [[1, 5, 3, 2, 1
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y = x-u^2
+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576
, -1265743/1048576], [-3235683/4194304, -3235683/4194304], [-29957/131072, -\
239655/1048576], [-2, -2]]]], [[1, 5, 3, 2, 2], [v < 0, And(-(v^2+1)^(1/2) < u
,u < v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [-772605/1048576
, -1545209/2097152]]]], [[1, 5, 3, 2, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v
), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/
1048576], [-1/4194304, -1/4194304]]]], [[1, 5, 3, 2, 4], [v < 0, And(-(v^2+1)^
(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [193151/
262144, 772605/1048576]]]], [[1, 5, 3, 2, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u
< v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [2, 2]]]], [[2,
8, 1, 5, 1], [v = 0, u = 1, x < -1, -x < y, z < 0], [regular_chain, [[0, 0], [
1, 1], [-2, -2], [3, 3], [-1, -1]]]], [[2, 8, 1, 5, 2], [v = 0, u = 1, x < -1,
-x < y, z = 0], [regular_chain, [[0, 0], [1, 1], [-2, -2], [3, 3], [0, 0]]]],
[[2, 8, 1, 5, 3], [v = 0, u = 1, x < -1, -x < y, 0 < z], [regular_chain, [[0,
0], [1, 1], [-2, -2], [3, 3], [1, 1]]]], [[2, 11, 7, 2, 1], [v = 0, 2^(1/2) <
u, u^2-1 < x, y = u^2-x-1, z = z], [regular_chain, [[0, 0], [3, 3], [9, 9], [-\
1, -1], [0, 0]]]], [[3, 11, 5, 4, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2
)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z = z], [regular_chain, [
[1, 1], [3299097/2097152, 3299097/2097152], [773191/1048576, 773191/1048576],
[275385/1048576, 137693/524288], [0, 0]]]], [[1, 11, 1, 4, 1], [v < 0, And((v^
2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x < -1, y = u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [-2, -2], [
2594957/1048576, 1297479/524288], [0, 0]]]], [[2, 1, 7, 1, 1], [v = 0, u < -2^
(1/2), u^2-1 < x, y < u^2-x-1, z = z], [regular_chain, [[0, 0], [-3, -3], [9,
9], [-2, -2], [0, 0]]]], [[3, 6, 3, 4, 1], [0 < v, u = -v, And(-1 < x,x < 1),
y = x+1, z < -1], [regular_chain, [[1, 1], [-1, -1], [0, 0], [1, 1], [-2, -2]]
]], [[3, 6, 3, 4, 2], [0 < v, u = -v, And(-1 < x,x < 1), y = x+1, z = -1], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [1, 1], [-1, -1]]]], [[3, 6, 3, 4, 3
], [0 < v, u = -v, And(-1 < x,x < 1), y = x+1, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [1, 1], [0, 0]]]], [[3, 6, 3, 4, 4],
[0 < v, u = -v, And(-1 < x,x < 1), y = x+1, z = 1], [regular_chain, [[1, 1], [
-1, -1], [0, 0], [1, 1], [1, 1]]]], [[3, 6, 3, 4, 5], [0 < v, u = -v, And(-1 <
x,x < 1), y = x+1, 1 < z], [regular_chain, [[1, 1], [-1, -1], [0, 0], [1, 1],
[2, 2]]]], [[3, 10, 3, 4, 1], [0 < v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y
= -x, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1/2
, -1/2], [1/2, 1/2], [-1, -1]]]], [[3, 10, 3, 4, 2], [0 < v, u = (v^2+1)^(1/2)
, And(-1 < x,x < 0), y = -x, z = 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [-1/2, -1/2], [1/2, 1/2], [0, 0]]]], [[3, 10, 3, 4, 3], [0 <
v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y = -x, 0 < z], [regular_chain, [[1,
1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [1/2, 1/2], [1, 1]]]], [[1
, 1, 5, 1, 1], [v < 0, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), y < x-u^2
+v^2+1, z = z], [regular_chain, [[-1, -1], [-3, -3], [4, 4], [-4, -4], [0, 0]]
]], [[1, 5, 3, 3, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^
2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [0, 0], [-2, -2]]]], [[1, 5, 3, 3, 2], [v < 0, And
(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [-\
772605/1048576, -1545209/2097152]]]], [[1, 5, 3, 3, 3], [v < 0, And(-(v^2+1)^(
1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-\
1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1
, -1], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/
4194304], [0, 0], [-1/4194304, -1/4194304]]]], [[1, 5, 3, 3, 4], [v < 0, And(-
(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u
^2-v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [
193151/262144, 772605/1048576]]]], [[1, 5, 3, 3, 5], [v < 0, And(-(v^2+1)^(1/2
) < u,u < v), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1),
(-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [2, 2]]]], [[2
, 8, 1, 4, 1], [v = 0, u = 1, x < -1, y = -x, z < 0], [regular_chain, [[0, 0],
[1, 1], [-2, -2], [2, 2], [-1, -1]]]], [[2, 8, 1, 4, 2], [v = 0, u = 1, x < -1
, y = -x, z = 0], [regular_chain, [[0, 0], [1, 1], [-2, -2], [2, 2], [0, 0]]]]
, [[2, 8, 1, 4, 3], [v = 0, u = 1, x < -1, y = -x, 0 < z], [regular_chain, [[0
, 0], [1, 1], [-2, -2], [2, 2], [1, 1]]]], [[2, 11, 7, 1, 1], [v = 0, 2^(1/2)
< u, u^2-1 < x, y < u^2-x-1, z = z], [regular_chain, [[0, 0], [3, 3], [9, 9],
[-2, -2], [0, 0]]]], [[3, 11, 5, 5, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2
+2)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = z], [regular_chain,
[[1, 1], [3299097/2097152, 3299097/2097152], [773191/1048576, 773191/1048576],
[2, 2], [0, 0]]]], [[1, 11, 1, 5, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2
)^(1/2)), x < -1, u^2-v^2-x-1 < y, z = z], [regular_chain, [[-1, -1], [3299097
/2097152, 3299097/2097152], [-2, -2], [4, 4], [0, 0]]]], [[2, 1, 7, 2, 1], [v
= 0, u < -2^(1/2), u^2-1 < x, y = u^2-x-1, z = z], [regular_chain, [[0, 0], [-\
3, -3], [9, 9], [-1, -1], [0, 0]]]], [[3, 6, 3, 3, 1], [0 < v, u = -v, And(-1
< x,x < 1), And(-1-x < y,y < x+1), z < -1], [regular_chain, [[1, 1], [-1, -1],
[0, 0], [0, 0], [-2, -2]]]], [[3, 6, 3, 3, 2], [0 < v, u = -v, And(-1 < x,x <
1), And(-1-x < y,y < x+1), z = -1], [regular_chain, [[1, 1], [-1, -1], [0, 0],
[0, 0], [-1, -1]]]], [[3, 6, 3, 3, 3], [0 < v, u = -v, And(-1 < x,x < 1), And(
-1-x < y,y < x+1), And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [0,
0], [0, 0], [0, 0]]]], [[3, 6, 3, 3, 4], [0 < v, u = -v, And(-1 < x,x < 1), 
And(-1-x < y,y < x+1), z = 1], [regular_chain, [[1, 1], [-1, -1], [0, 0], [0,
0], [1, 1]]]], [[3, 6, 3, 3, 5], [0 < v, u = -v, And(-1 < x,x < 1), And(-1-x <
y,y < x+1), 1 < z], [regular_chain, [[1, 1], [-1, -1], [0, 0], [0, 0], [2, 2]]
]], [[3, 10, 3, 3, 1], [0 < v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), And(x < y
,y < -x), z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [
-1/2, -1/2], [0, 0], [-1, -1]]]], [[3, 10, 3, 3, 2], [0 < v, u = (v^2+1)^(1/2)
, And(-1 < x,x < 0), And(x < y,y < -x), z = 0], [regular_chain, [[1, 1], [
741455/524288, 1482911/1048576], [-1/2, -1/2], [0, 0], [0, 0]]]], [[3, 10, 3,
3, 3], [0 < v, u = (v^2+1)^(1/2), And(-1 < x,x < 0), And(x < y,y < -x), 0 < z]
, [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [0,
0], [1, 1]]]], [[1, 11, 5, 1, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1
/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = z], [regular_chain, [[-1,
-1], [3299097/2097152, 3299097/2097152], [773191/1048576, 773191/1048576], [-2
, -2], [0, 0]]]], [[2, 2, 2, 2, 1], [v = 0, u = -2^(1/2), x = -1, y = -2, z =
z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [-1, -1], [-2
, -2], [0, 0]]]], [[3, 6, 3, 1, 1], [0 < v, u = -v, And(-1 < x,x < 1), y < -1-
x, z < -1], [regular_chain, [[1, 1], [-1, -1], [0, 0], [-2, -2], [-2, -2]]]],
[[3, 6, 3, 1, 2], [0 < v, u = -v, And(-1 < x,x < 1), y < -1-x, z = -1], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [-2, -2], [-1, -1]]]], [[3, 6, 3, 1,
3], [0 < v, u = -v, And(-1 < x,x < 1), y < -1-x, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [-2, -2], [0, 0]]]], [[3, 6, 3, 1, 4
], [0 < v, u = -v, And(-1 < x,x < 1), y < -1-x, z = 1], [regular_chain, [[1, 1
], [-1, -1], [0, 0], [-2, -2], [1, 1]]]], [[3, 6, 3, 1, 5], [0 < v, u = -v, 
And(-1 < x,x < 1), y < -1-x, 1 < z], [regular_chain, [[1, 1], [-1, -1], [0, 0]
, [-2, -2], [2, 2]]]], [[3, 10, 2, 2, 1], [0 < v, u = (v^2+1)^(1/2), x = -1, y
= -1, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1,
-1], [-1, -1], [-1, -1]]]], [[3, 10, 2, 2, 2], [0 < v, u = (v^2+1)^(1/2), x =
-1, y = -1, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576],
[-1, -1], [-1, -1], [0, 0]]]], [[3, 10, 2, 2, 3], [0 < v, u = (v^2+1)^(1/2), x
= -1, y = -1, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576
], [-1, -1], [-1, -1], [1, 1]]]], [[1, 1, 6, 2, 1], [v < 0, u < -(v^2+2)^(1/2)
, x = u^2-v^2-1, y = 0, z = z], [regular_chain, [[-1, -1], [-3, -3], [7, 7], [
0, 0], [0, 0]]]], [[1, 5, 3, 5, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And
(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [-2, -2]]]], [[1, 5, 3, 5, 2], [v < 0, And
(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = -(
-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [2, 2], [-772605/1048576, -\
1545209/2097152]]]], [[1, 5, 3, 5, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v),
And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-
u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [2, 2], [-1/4194304, -1/
4194304]]]], [[1, 5, 3, 5, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(-1 <
x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/
4194304], [2, 2], [193151/262144, 772605/1048576]]]], [[1, 5, 3, 5, 5], [v < 0
, And(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, (
-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743
/1048576], [-3235683/4194304, -3235683/4194304], [2, 2], [2, 2]]]], [[2, 7, 6,
4, 1], [v = 0, And(0 < u,u < 1), x = 1, y = -u^2+2, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [7/4, 7/4], [-2, -2]]]], [[2, 7, 6
, 4, 2], [v = 0, And(0 < u,u < 1), x = 1, y = -u^2+2, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [7/4, 7/4], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 6, 4, 3], [v = 0, And(0 < u,u < 1), x = 1, y = -u
^2+2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [
1/2, 1/2], [1, 1], [7/4, 7/4], [-1/8388608, -1/8388608]]]], [[2, 7, 6, 4, 4],
[v = 0, And(0 < u,u < 1), x = 1, y = -u^2+2, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [7/4, 7/4], [908093/1048576, 
454047/524288]]]], [[2, 7, 6, 4, 5], [v = 0, And(0 < u,u < 1), x = 1, y = -u^2
+2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [7/4, 7/
4], [2, 2]]]], [[2, 11, 3, 5, 1], [v = 0, 2^(1/2) < u, And(-1 < x,x < 1), u^2-
x-1 < y, z = z], [regular_chain, [[0, 0], [3, 3], [0, 0], [9, 9], [0, 0]]]], [
[3, 11, 7, 1, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), 1 < x, y <
u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/
2097152], [2, 2], [-3, -3], [0, 0]]]], [[1, 11, 4, 3, 1], [v < 0, And((v^2+1)^
(1/2) < u,u < (v^2+2)^(1/2)), x = u^2-v^2-1, 0 < y, z = z], [regular_chain, [[
-1, -1], [3299097/2097152, 3299097/2097152], [497805/1048576, 248903/524288],
[1, 1], [0, 0]]]], [[2, 2, 2, 1, 1], [v = 0, u = -2^(1/2), x = -1, y < -2, z =
z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [-1, -1], [-3
, -3], [0, 0]]]], [[3, 6, 3, 2, 1], [0 < v, u = -v, And(-1 < x,x < 1), y = -1-
x, z < -1], [regular_chain, [[1, 1], [-1, -1], [0, 0], [-1, -1], [-2, -2]]]],
[[3, 6, 3, 2, 2], [0 < v, u = -v, And(-1 < x,x < 1), y = -1-x, z = -1], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [-1, -1], [-1, -1]]]], [[3, 6, 3, 2,
3], [0 < v, u = -v, And(-1 < x,x < 1), y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [0, 0], [-1, -1], [0, 0]]]], [[3, 6, 3, 2, 4
], [0 < v, u = -v, And(-1 < x,x < 1), y = -1-x, z = 1], [regular_chain, [[1, 1
], [-1, -1], [0, 0], [-1, -1], [1, 1]]]], [[3, 6, 3, 2, 5], [0 < v, u = -v, 
And(-1 < x,x < 1), y = -1-x, 1 < z], [regular_chain, [[1, 1], [-1, -1], [0, 0]
, [-1, -1], [2, 2]]]], [[3, 10, 2, 3, 1], [0 < v, u = (v^2+1)^(1/2), x = -1, 
And(-1 < y,y < 1), z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [-1, -1], [0, 0], [-1, -1]]]], [[3, 10, 2, 3, 2], [0 < v, u = (v^2+1
)^(1/2), x = -1, And(-1 < y,y < 1), z = 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-1, -1], [0, 0], [0, 0]]]], [[3, 10, 2, 3, 3], [0 <
v, u = (v^2+1)^(1/2), x = -1, And(-1 < y,y < 1), 0 < z], [regular_chain, [[1,
1], [741455/524288, 1482911/1048576], [-1, -1], [0, 0], [1, 1]]]], [[1, 1, 6,
1, 1], [v < 0, u < -(v^2+2)^(1/2), x = u^2-v^2-1, y < 0, z = z], [
regular_chain, [[-1, -1], [-3, -3], [7, 7], [-1, -1], [0, 0]]]], [[1, 5, 3, 4,
1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y = u^2-
v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304], [239655/
1048576, 29957/131072], [-2, -2]]]], [[1, 5, 3, 4, 2], [v < 0, And(-(v^2+1)^(1
/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^
(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [239655/1048576, 29957/131072], [-772605/
1048576, -1545209/2097152]]]], [[1, 5, 3, 4, 3], [v < 0, And(-(v^2+1)^(1/2) <
u,u < v), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-3235683/4194304, -3235683/4194304], [239655/1048576, 29957
/131072], [-1/4194304, -1/4194304]]]], [[1, 5, 3, 4, 4], [v < 0, And(-(v^2+1)^
(1/2) < u,u < v), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [239655/1048576, 29957/131072], [193151/
262144, 772605/1048576]]]], [[1, 5, 3, 4, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u
< v), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [239655/1048576, 29957/131072], [2, 2]]]], [[2, 7,
6, 5, 1], [v = 0, And(0 < u,u < 1), x = 1, -u^2+2 < y, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [3, 3], [-2, -2]]]], [[2, 7, 6, 5,
2], [v = 0, And(0 < u,u < 1), x = 1, -u^2+2 < y, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [3, 3], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 6, 5, 3], [v = 0, And(0 < u,u < 1), x = 1, -u^2+2
< y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1
/2, 1/2], [1, 1], [3, 3], [-1/8388608, -1/8388608]]]], [[2, 7, 6, 5, 4], [v =
0, And(0 < u,u < 1), x = 1, -u^2+2 < y, z = (-u^2+1)^(1/2)], [regular_chain, [
[0, 0], [1/2, 1/2], [1, 1], [3, 3], [908093/1048576, 454047/524288]]]], [[2, 7
, 6, 5, 5], [v = 0, And(0 < u,u < 1), x = 1, -u^2+2 < y, (-u^2+1)^(1/2) < z],
[regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [3, 3], [2, 2]]]], [[2, 11, 4, 1,
1], [v = 0, 2^(1/2) < u, x = 1, y < -u^2+2, z = z], [regular_chain, [[0, 0], [
3, 3], [1, 1], [-8, -8], [0, 0]]]], [[3, 11, 6, 5, 1], [0 < v, And((v^2+1)^(1/
2) < u,u < (v^2+2)^(1/2)), x = 1, -u^2+v^2+2 < y, z = z], [regular_chain, [[1,
1], [3299097/2097152, 3299097/2097152], [1, 1], [2, 2], [0, 0]]]], [[1, 11, 4,
2, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = u^2-v^2-1, y = 0,
z = z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [497805
/1048576, 248903/524288], [0, 0], [0, 0]]]], [[2, 2, 2, 4, 1], [v = 0, u = -2^
(1/2), x = -1, y = 2, z = z], [regular_chain, [[0, 0], [-1482911/1048576, -\
741455/524288], [-1, -1], [2, 2], [0, 0]]]], [[3, 6, 2, 2, 1], [0 < v, u = -v,
x = -1, y = 0, z < -1], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [0, 0], [
-2, -2]]]], [[3, 6, 2, 2, 2], [0 < v, u = -v, x = -1, y = 0, z = -1], [
regular_chain, [[1, 1], [-1, -1], [-1, -1], [0, 0], [-1, -1]]]], [[3, 6, 2, 2,
3], [0 < v, u = -v, x = -1, y = 0, And(-1 < z,z < 1)], [regular_chain, [[1, 1]
, [-1, -1], [-1, -1], [0, 0], [0, 0]]]], [[3, 6, 2, 2, 4], [0 < v, u = -v, x =
-1, y = 0, z = 1], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [0, 0], [1, 1]
]]], [[3, 6, 2, 2, 5], [0 < v, u = -v, x = -1, y = 0, 1 < z], [regular_chain,
[[1, 1], [-1, -1], [-1, -1], [0, 0], [2, 2]]]], [[3, 10, 2, 4, 1], [0 < v, u =
(v^2+1)^(1/2), x = -1, y = 1, z < 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [-1, -1], [1, 1], [-1, -1]]]], [[3, 10, 2, 4, 2], [0 < v, u
= (v^2+1)^(1/2), x = -1, y = 1, z = 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-1, -1], [1, 1], [0, 0]]]], [[3, 10, 2, 4, 3], [0 <
v, u = (v^2+1)^(1/2), x = -1, y = 1, 0 < z], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-1, -1], [1, 1], [1, 1]]]], [[1, 1, 5, 5, 1], [v <
0, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = z], [
regular_chain, [[-1, -1], [-3, -3], [4, 4], [4, 4], [0, 0]]]], [[1, 5, 4, 2, 1
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y = 0, z < -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [
-1138531/2097152, -569265/1048576], [0, 0], [-2, -2]]]], [[1, 5, 4, 2, 2], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y = 0, z = -(-u^2+v^2+1)^(1
/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-\
1138531/2097152, -569265/1048576], [0, 0], [-772605/1048576, -1545209/2097152]
]]], [[1, 5, 4, 2, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y
= 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-\
1, -1], [-1265743/1048576, -1265743/1048576], [-1138531/2097152, -569265/
1048576], [0, 0], [-1/4194304, -1/4194304]]]], [[1, 5, 4, 2, 4], [v < 0, And(-
(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y = 0, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1138531/
2097152, -569265/1048576], [0, 0], [193151/262144, 772605/1048576]]]], [[1, 5,
4, 2, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y = 0, (-u^2+v
^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-1138531/2097152, -569265/1048576], [0, 0], [2, 2]]]], [[2, 7, 6, 2
, 1], [v = 0, And(0 < u,u < 1), x = 1, y = u^2-2, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-7/4, -7/4], [-2, -2]]]], [[2, 7,
6, 2, 2], [v = 0, And(0 < u,u < 1), x = 1, y = u^2-2, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-7/4, -7/4], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 6, 2, 3], [v = 0, And(0 < u,u < 1), x = 1, y = u^
2-2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1
/2, 1/2], [1, 1], [-7/4, -7/4], [-1/8388608, -1/8388608]]]], [[2, 7, 6, 2, 4],
[v = 0, And(0 < u,u < 1), x = 1, y = u^2-2, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-7/4, -7/4], [908093/1048576, 
454047/524288]]]], [[2, 7, 6, 2, 5], [v = 0, And(0 < u,u < 1), x = 1, y = u^2-\
2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [-7/4, -7
/4], [2, 2]]]], [[2, 11, 4, 2, 1], [v = 0, 2^(1/2) < u, x = 1, y = -u^2+2, z =
z], [regular_chain, [[0, 0], [3, 3], [1, 1], [-7, -7], [0, 0]]]], [[3, 11, 6,
4, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = 1, y = -u^2+v^2+2
, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [1, 1],
[275385/524288, 550771/1048576], [0, 0]]]], [[1, 11, 4, 1, 1], [v < 0, And((v^
2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = u^2-v^2-1, y < 0, z = z], [
regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [497805/1048576,
248903/524288], [-1, -1], [0, 0]]]], [[2, 2, 2, 3, 1], [v = 0, u = -2^(1/2), x
= -1, And(-2 < y,y < 2), z = z], [regular_chain, [[0, 0], [-1482911/1048576, -\
741455/524288], [-1, -1], [0, 0], [0, 0]]]], [[3, 6, 2, 3, 1], [0 < v, u = -v,
x = -1, 0 < y, z < -1], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [1, 1], [
-2, -2]]]], [[3, 6, 2, 3, 2], [0 < v, u = -v, x = -1, 0 < y, z = -1], [
regular_chain, [[1, 1], [-1, -1], [-1, -1], [1, 1], [-1, -1]]]], [[3, 6, 2, 3,
3], [0 < v, u = -v, x = -1, 0 < y, And(-1 < z,z < 1)], [regular_chain, [[1, 1]
, [-1, -1], [-1, -1], [1, 1], [0, 0]]]], [[3, 6, 2, 3, 4], [0 < v, u = -v, x =
-1, 0 < y, z = 1], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [1, 1], [1, 1]
]]], [[3, 6, 2, 3, 5], [0 < v, u = -v, x = -1, 0 < y, 1 < z], [regular_chain,
[[1, 1], [-1, -1], [-1, -1], [1, 1], [2, 2]]]], [[3, 10, 2, 5, 1], [0 < v, u =
(v^2+1)^(1/2), x = -1, 1 < y, z < 0], [regular_chain, [[1, 1], [741455/524288,
1482911/1048576], [-1, -1], [2, 2], [-1, -1]]]], [[3, 10, 2, 5, 2], [0 < v, u
= (v^2+1)^(1/2), x = -1, 1 < y, z = 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-1, -1], [2, 2], [0, 0]]]], [[3, 10, 2, 5, 3], [0 <
v, u = (v^2+1)^(1/2), x = -1, 1 < y, 0 < z], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-1, -1], [2, 2], [1, 1]]]], [[1, 1, 5, 4, 1], [v <
0, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [-3, -3], [4, 4], [3, 3], [0, 0]]]], [[1, 5, 4, 1, 1
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y < 0, z < -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [
-1138531/2097152, -569265/1048576], [-1, -1], [-2, -2]]]], [[1, 5, 4, 1, 2], [
v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y < 0, z = -(-u^2+v^2+1)^
(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-\
1138531/2097152, -569265/1048576], [-1, -1], [-772605/1048576, -1545209/
2097152]]]], [[1, 5, 4, 1, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-
v^2-1, y < 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1138531/
2097152, -569265/1048576], [-1, -1], [-1/4194304, -1/4194304]]]], [[1, 5, 4, 1
, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y < 0, z = (-u^2+v
^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576],
[-1138531/2097152, -569265/1048576], [-1, -1], [193151/262144, 772605/1048576]
]]], [[1, 5, 4, 1, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, y
< 0, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-1138531/2097152, -569265/1048576], [-1, -1], [2, 2]]]], [[
2, 7, 6, 3, 1], [v = 0, And(0 < u,u < 1), x = 1, And(u^2-2 < y,y < -u^2+2), z
< -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [0, 0], [-2,
-2]]]], [[2, 7, 6, 3, 2], [v = 0, And(0 < u,u < 1), x = 1, And(u^2-2 < y,y < -
u^2+2), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [0,
0], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 6, 3, 3], [v = 0, And(0 <
u,u < 1), x = 1, And(u^2-2 < y,y < -u^2+2), And(-(-u^2+1)^(1/2) < z,z < (-u^2+
1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [0, 0], [-1/8388608,
-1/8388608]]]], [[2, 7, 6, 3, 4], [v = 0, And(0 < u,u < 1), x = 1, And(u^2-2 <
y,y < -u^2+2), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [1, 1
], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 7, 6, 3, 5], [v = 0, And(0
< u,u < 1), x = 1, And(u^2-2 < y,y < -u^2+2), (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [1/2, 1/2], [1, 1], [0, 0], [2, 2]]]], [[2, 11, 4, 3,
1], [v = 0, 2^(1/2) < u, x = 1, And(-u^2+2 < y,y < u^2-2), z = z], [
regular_chain, [[0, 0], [3, 3], [1, 1], [0, 0], [0, 0]]]], [[3, 11, 6, 3, 1],
[0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = 1, And(u^2-v^2-2 < y,y <
-u^2+v^2+2), z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/
2097152], [1, 1], [0, 0], [0, 0]]]], [[1, 1, 7, 3, 1], [v < 0, u < -(v^2+2)^(1
/2), u^2-v^2-1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [
regular_chain, [[-1, -1], [-3, -3], [8, 8], [0, 0], [0, 0]]]], [[1, 5, 5, 1, 1
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y < u^2-v^
2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576,
-1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2], [-2, -2]]]], [[
1, 5, 5, 1, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1
), y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2]
, [-772605/1048576, -1545209/2097152]]]], [[1, 5, 5, 1, 3], [v < 0, And(-(v^2+
1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, And(-(-u^2+v^2
+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2], [-1/
4194304, -1/4194304]]]], [[1, 5, 5, 1, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u <
v), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [-2, -2], [193151/262144, 772605/1048576]]]], [[1, 5
, 5, 1, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y
< u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2], [2, 2]
]]], [[2, 7, 7, 3, 1], [v = 0, And(0 < u,u < 1), 1 < x, And(u^2-x-1 < y,y < x-
u^2+1), z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [0,
0], [-2, -2]]]], [[2, 7, 7, 3, 2], [v = 0, And(0 < u,u < 1), 1 < x, And(u^2-x-\
1 < y,y < x-u^2+1), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2],
[2, 2], [0, 0], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 7, 3, 3], [v
= 0, And(0 < u,u < 1), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), And(-(-u^2+1)^(1/2
) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [0, 0
], [-1/8388608, -1/8388608]]]], [[2, 7, 7, 3, 4], [v = 0, And(0 < u,u < 1), 1
< x, And(u^2-x-1 < y,y < x-u^2+1), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0
], [1/2, 1/2], [2, 2], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 7, 7,
3, 5], [v = 0, And(0 < u,u < 1), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), (-u^2+1)
^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [0, 0], [2, 2]]]], [
[2, 11, 4, 4, 1], [v = 0, 2^(1/2) < u, x = 1, y = u^2-2, z = z], [
regular_chain, [[0, 0], [3, 3], [1, 1], [7, 7], [0, 0]]]], [[3, 11, 7, 5, 1],
[0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), 1 < x, x-u^2+v^2+1 < y, z =
z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [2, 2], [3, 3
], [0, 0]]]], [[1, 11, 3, 5, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/
2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = z], [regular_chain, [[-1,
-1], [3299097/2097152, 3299097/2097152], [-550771/2097152, -550771/2097152], [
2, 2], [0, 0]]]], [[2, 2, 1, 3, 1], [v = 0, u = -2^(1/2), x < -1, And(x-1 < y,
y < 1-x), z = z], [regular_chain, [[0, 0], [-1482911/1048576, -741455/524288],
[-2, -2], [0, 0], [0, 0]]]], [[3, 6, 1, 5, 1], [0 < v, u = -v, x < -1, -1-x <
y, z < -1], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [2, 2], [-2, -2]]]],
[[3, 6, 1, 5, 2], [0 < v, u = -v, x < -1, -1-x < y, z = -1], [regular_chain, [
[1, 1], [-1, -1], [-2, -2], [2, 2], [-1, -1]]]], [[3, 6, 1, 5, 3], [0 < v, u =
-v, x < -1, -1-x < y, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [
-2, -2], [2, 2], [0, 0]]]], [[3, 6, 1, 5, 4], [0 < v, u = -v, x < -1, -1-x < y
, z = 1], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [2, 2], [1, 1]]]], [[3,
6, 1, 5, 5], [0 < v, u = -v, x < -1, -1-x < y, 1 < z], [regular_chain, [[1, 1]
, [-1, -1], [-2, -2], [2, 2], [2, 2]]]], [[3, 10, 1, 3, 1], [0 < v, u = (v^2+1
)^(1/2), x < -1, And(x < y,y < -x), z < 0], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-2, -2], [0, 0], [-1, -1]]]], [[3, 10, 1, 3, 2], [0
< v, u = (v^2+1)^(1/2), x < -1, And(x < y,y < -x), z = 0], [regular_chain, [[1
, 1], [741455/524288, 1482911/1048576], [-2, -2], [0, 0], [0, 0]]]], [[3, 10,
1, 3, 3], [0 < v, u = (v^2+1)^(1/2), x < -1, And(x < y,y < -x), 0 < z], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-2, -2], [0, 0], [1
, 1]]]], [[1, 1, 7, 2, 1], [v < 0, u < -(v^2+2)^(1/2), u^2-v^2-1 < x, y = u^2-
v^2-x-1, z = z], [regular_chain, [[-1, -1], [-3, -3], [8, 8], [-1, -1], [0, 0]
]]], [[1, 5, 4, 3, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, 0
< y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [-2, -2]]]], [[
1, 5, 4, 3, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, 0 < y, z
= -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743
/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [-772605/1048576, -\
1545209/2097152]]]], [[1, 5, 4, 3, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v),
x = u^2-v^2-1, 0 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-1138531/
2097152, -569265/1048576], [1, 1], [-1/4194304, -1/4194304]]]], [[1, 5, 4, 3,
4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, 0 < y, z = (-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [
-1138531/2097152, -569265/1048576], [1, 1], [193151/262144, 772605/1048576]]]]
, [[1, 5, 4, 3, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x = u^2-v^2-1, 0 <
y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -\
1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [2, 2]]]], [[2,
7, 7, 4, 1], [v = 0, And(0 < u,u < 1), 1 < x, y = x-u^2+1, z < -(-u^2+1)^(1/2)
], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [11/4, 11/4], [-2, -2]]]], [[2
, 7, 7, 4, 2], [v = 0, And(0 < u,u < 1), 1 < x, y = x-u^2+1, z = -(-u^2+1)^(1/
2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [11/4, 11/4], [-1816187/
2097152, -3632373/4194304]]]], [[2, 7, 7, 4, 3], [v = 0, And(0 < u,u < 1), 1 <
x, y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain,
[[0, 0], [1/2, 1/2], [2, 2], [11/4, 11/4], [-1/8388608, -1/8388608]]]], [[2, 7
, 7, 4, 4], [v = 0, And(0 < u,u < 1), 1 < x, y = x-u^2+1, z = (-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [11/4, 11/4], [908093/1048576, 
454047/524288]]]], [[2, 7, 7, 4, 5], [v = 0, And(0 < u,u < 1), 1 < x, y = x-u^
2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [11/4,
11/4], [2, 2]]]], [[2, 11, 4, 5, 1], [v = 0, 2^(1/2) < u, x = 1, u^2-2 < y, z
= z], [regular_chain, [[0, 0], [3, 3], [1, 1], [8, 8], [0, 0]]]], [[3, 11, 7,
4, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), 1 < x, y = x-u^2+v^2+
1, z = z], [regular_chain, [[1, 1], [3299097/2097152, 3299097/2097152], [2, 2]
, [799673/524288, 1599347/1048576], [0, 0]]]], [[1, 11, 3, 4, 1], [v < 0, And(
(v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x
-1, z = z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [-\
550771/2097152, -550771/2097152], [773191/1048576, 96649/131072], [0, 0]]]], [
[2, 2, 1, 2, 1], [v = 0, u = -2^(1/2), x < -1, y = x-1, z = z], [regular_chain
, [[0, 0], [-1482911/1048576, -741455/524288], [-2, -2], [-3, -3], [0, 0]]]],
[[3, 6, 2, 1, 1], [0 < v, u = -v, x = -1, y < 0, z < -1], [regular_chain, [[1,
1], [-1, -1], [-1, -1], [-1, -1], [-2, -2]]]], [[3, 6, 2, 1, 2], [0 < v, u = -
v, x = -1, y < 0, z = -1], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [-1, -\
1], [-1, -1]]]], [[3, 6, 2, 1, 3], [0 < v, u = -v, x = -1, y < 0, And(-1 < z,z
< 1)], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [-1, -1], [0, 0]]]], [[3,
6, 2, 1, 4], [0 < v, u = -v, x = -1, y < 0, z = 1], [regular_chain, [[1, 1], [
-1, -1], [-1, -1], [-1, -1], [1, 1]]]], [[3, 6, 2, 1, 5], [0 < v, u = -v, x =
-1, y < 0, 1 < z], [regular_chain, [[1, 1], [-1, -1], [-1, -1], [-1, -1], [2,
2]]]], [[3, 10, 1, 4, 1], [0 < v, u = (v^2+1)^(1/2), x < -1, y = -x, z < 0], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-2, -2], [2, 2], [-\
1, -1]]]], [[3, 10, 1, 4, 2], [0 < v, u = (v^2+1)^(1/2), x < -1, y = -x, z = 0
], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-2, -2], [2, 2]
, [0, 0]]]], [[3, 10, 1, 4, 3], [0 < v, u = (v^2+1)^(1/2), x < -1, y = -x, 0 <
z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-2, -2], [2, 2
], [1, 1]]]], [[1, 1, 7, 1, 1], [v < 0, u < -(v^2+2)^(1/2), u^2-v^2-1 < x, y <
u^2-v^2-x-1, z = z], [regular_chain, [[-1, -1], [-3, -3], [8, 8], [-2, -2], [0
, 0]]]], [[1, 5, 5, 3, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-\
1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [-3/8388608, -3/8388608], [-2, -2]]]], [[1, 5, 5, 3,
2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), And(u^2-v
^2-x-1 < y,y < x-u^2+v^2+1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -\
1], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-\
3/8388608, -3/8388608], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 5, 3,
3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), And(u^2-v
^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2
))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [-3/8388608, -3/8388608], [-1/4194304, -1/4194304]]]
], [[1, 5, 5, 3, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,
x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [-3/8388608, -3/8388608], [193151/262144, 772605/
1048576]]]], [[1, 5, 5, 3, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-
v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z
], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [-3/8388608, -3/8388608], [2, 2]]]], [[2, 7, 7, 1, 1
], [v = 0, And(0 < u,u < 1), 1 < x, y < u^2-x-1, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-4, -4], [-2, -2]]]], [[2, 7, 7,
1, 2], [v = 0, And(0 < u,u < 1), 1 < x, y < u^2-x-1, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-4, -4], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 7, 1, 3], [v = 0, And(0 < u,u < 1), 1 < x, y < u^
2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0],
[1/2, 1/2], [2, 2], [-4, -4], [-1/8388608, -1/8388608]]]], [[2, 7, 7, 1, 4], [
v = 0, And(0 < u,u < 1), 1 < x, y < u^2-x-1, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-4, -4], [908093/1048576, 454047/
524288]]]], [[2, 7, 7, 1, 5], [v = 0, And(0 < u,u < 1), 1 < x, y < u^2-x-1, (-
u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-4, -4], [2,
2]]]], [[2, 11, 5, 1, 1], [v = 0, 2^(1/2) < u, And(1 < x,x < u^2-1), y < x-u^2
+1, z = z], [regular_chain, [[0, 0], [3, 3], [9/2, 9/2], [-5, -5], [0, 0]]]],
[[3, 11, 7, 3, 1], [0 < v, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), 1 < x, 
And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [regular_chain, [[1, 1], [
3299097/2097152, 3299097/2097152], [2, 2], [0, 0], [0, 0]]]], [[1, 11, 3, 3, 1
], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(-1 < x,x < u^2-v^2-1)
, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[-1, -1], [
3299097/2097152, 3299097/2097152], [-550771/2097152, -550771/2097152], [0, 0],
[0, 0]]]], [[2, 2, 1, 5, 1], [v = 0, u = -2^(1/2), x < -1, 1-x < y, z = z], [
regular_chain, [[0, 0], [-1482911/1048576, -741455/524288], [-2, -2], [4, 4],
[0, 0]]]], [[3, 6, 1, 3, 1], [0 < v, u = -v, x < -1, And(x+1 < y,y < -1-x), z
< -1], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [0, 0], [-2, -2]]]], [[3,
6, 1, 3, 2], [0 < v, u = -v, x < -1, And(x+1 < y,y < -1-x), z = -1], [
regular_chain, [[1, 1], [-1, -1], [-2, -2], [0, 0], [-1, -1]]]], [[3, 6, 1, 3,
3], [0 < v, u = -v, x < -1, And(x+1 < y,y < -1-x), And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [-2, -2], [0, 0], [0, 0]]]], [[3, 6, 1, 3, 4
], [0 < v, u = -v, x < -1, And(x+1 < y,y < -1-x), z = 1], [regular_chain, [[1,
1], [-1, -1], [-2, -2], [0, 0], [1, 1]]]], [[3, 6, 1, 3, 5], [0 < v, u = -v, x
< -1, And(x+1 < y,y < -1-x), 1 < z], [regular_chain, [[1, 1], [-1, -1], [-2, -\
2], [0, 0], [2, 2]]]], [[3, 10, 1, 5, 1], [0 < v, u = (v^2+1)^(1/2), x < -1, -
x < y, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-2,
-2], [3, 3], [-1, -1]]]], [[3, 10, 1, 5, 2], [0 < v, u = (v^2+1)^(1/2), x < -1
, -x < y, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [
-2, -2], [3, 3], [0, 0]]]], [[3, 10, 1, 5, 3], [0 < v, u = (v^2+1)^(1/2), x <
-1, -x < y, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576],
[-2, -2], [3, 3], [1, 1]]]], [[1, 1, 6, 3, 1], [v < 0, u < -(v^2+2)^(1/2), x =
u^2-v^2-1, 0 < y, z = z], [regular_chain, [[-1, -1], [-3, -3], [7, 7], [1, 1],
[0, 0]]]], [[1, 5, 5, 2, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^
2-1 < x,x < 1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-\
1, -1], [-1265743/1048576, -1265743/1048576], [479311/2097152, 479311/2097152]
, [-808921/1048576, -3235683/4194304], [-2, -2]]]], [[1, 5, 5, 2, 2], [v < 0,
And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304
], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 5, 2, 3], [v < 0, And(-(v^2
+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, And(-(-u^2+v^
2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [479311/2097152, 479311/2097152], [-808921/1048576
, -3235683/4194304], [-1/4194304, -1/4194304]]]], [[1, 5, 5, 2, 4], [v < 0, 
And(-(v^2+1)^(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304
], [193151/262144, 772605/1048576]]]], [[1, 5, 5, 2, 5], [v < 0, And(-(v^2+1)^
(1/2) < u,u < v), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2
) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [
479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304], [2, 2]]]
], [[2, 7, 7, 2, 1], [v = 0, And(0 < u,u < 1), 1 < x, y = u^2-x-1, z < -(-u^2+
1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-11/4, -11/4], [-2, -\
2]]]], [[2, 7, 7, 2, 2], [v = 0, And(0 < u,u < 1), 1 < x, y = u^2-x-1, z = -(-
u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-11/4, -11/4], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 7, 7, 2, 3], [v = 0, And(0 < u,u <
1), 1 < x, y = u^2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-11/4, -11/4], [-1/8388608, -1/
8388608]]]], [[2, 7, 7, 2, 4], [v = 0, And(0 < u,u < 1), 1 < x, y = u^2-x-1, z
= (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [2, 2], [-11/4, -11/4]
, [908093/1048576, 454047/524288]]]], [[2, 7, 7, 2, 5], [v = 0, And(0 < u,u <
1), 1 < x, y = u^2-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/
2], [2, 2], [-11/4, -11/4], [2, 2]]]], [[2, 11, 5, 2, 1], [v = 0, 2^(1/2) < u,
And(1 < x,x < u^2-1), y = x-u^2+1, z = z], [regular_chain, [[0, 0], [3, 3], [9
/2, 9/2], [-7/2, -7/2], [0, 0]]]], [[3, 11, 7, 2, 1], [0 < v, And((v^2+1)^(1/2
) < u,u < (v^2+2)^(1/2)), 1 < x, y = u^2-v^2-x-1, z = z], [regular_chain, [[1,
1], [3299097/2097152, 3299097/2097152], [2, 2], [-3198693/2097152, -799673/
524288], [0, 0]]]], [[1, 11, 3, 2, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+
2)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = z], [regular_chain,
[[-1, -1], [3299097/2097152, 3299097/2097152], [-550771/2097152, -550771/
2097152], [-1546383/2097152, -773191/1048576], [0, 0]]]], [[2, 2, 1, 4, 1], [v
= 0, u = -2^(1/2), x < -1, y = 1-x, z = z], [regular_chain, [[0, 0], [-1482911
/1048576, -741455/524288], [-2, -2], [3, 3], [0, 0]]]], [[3, 6, 1, 4, 1], [0 <
v, u = -v, x < -1, y = -1-x, z < -1], [regular_chain, [[1, 1], [-1, -1], [-2,
-2], [1, 1], [-2, -2]]]], [[3, 6, 1, 4, 2], [0 < v, u = -v, x < -1, y = -1-x,
z = -1], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [1, 1], [-1, -1]]]], [[3
, 6, 1, 4, 3], [0 < v, u = -v, x < -1, y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [-2, -2], [1, 1], [0, 0]]]], [[3, 6, 1, 4, 4
], [0 < v, u = -v, x < -1, y = -1-x, z = 1], [regular_chain, [[1, 1], [-1, -1]
, [-2, -2], [1, 1], [1, 1]]]], [[3, 6, 1, 4, 5], [0 < v, u = -v, x < -1, y = -\
1-x, 1 < z], [regular_chain, [[1, 1], [-1, -1], [-2, -2], [1, 1], [2, 2]]]], [
[3, 10, 2, 1, 1], [0 < v, u = (v^2+1)^(1/2), x = -1, y < -1, z < 0], [
regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1, -1], [-2, -2],
[-1, -1]]]], [[3, 10, 2, 1, 2], [0 < v, u = (v^2+1)^(1/2), x = -1, y < -1, z =
0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1, -1], [-2,
-2], [0, 0]]]], [[3, 10, 2, 1, 3], [0 < v, u = (v^2+1)^(1/2), x = -1, y < -1,
0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-1, -1], [
-2, -2], [1, 1]]]], [[1, 2, 1, 3, 1], [v < 0, u = -(v^2+2)^(1/2), x < -1, And(
x-1 < y,y < 1-x), z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -\
3632373/2097152], [-2, -2], [0, 0], [0, 0]]]], [[1, 7, 1, 4, 1], [v < 0, And(v
< u,u < -v), x < u^2-v^2-1, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-3, -3], [1, 1], [-3, -3]]]], [[1, 7, 1, 4,
2], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, y = u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [1, 1], [-1482911/
1048576, -741455/524288]]]], [[1, 7, 1, 4, 3], [v < 0, And(v < u,u < -v), x <
u^2-v^2-1, y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2)
)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [1, 1], [0, 0]]]], [[1, 7, 1,
4, 4], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, y = u^2-v^2-x-1, z = (-u^2+v^
2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [1, 1], [741455/
524288, 1482911/1048576]]]], [[1, 7, 1, 4, 5], [v < 0, And(v < u,u < -v), x <
u^2-v^2-1, y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1]
, [0, 0], [-3, -3], [1, 1], [3, 3]]]], [[2, 8, 5, 3, 1], [v = 0, u = 1, And(0
< x,x < 1), And(-x < y,y < x), z < 0], [regular_chain, [[0, 0], [1, 1], [1/2,
1/2], [0, 0], [-1, -1]]]], [[2, 8, 5, 3, 2], [v = 0, u = 1, And(0 < x,x < 1),
And(-x < y,y < x), z = 0], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [0, 0]
, [0, 0]]]], [[2, 8, 5, 3, 3], [v = 0, u = 1, And(0 < x,x < 1), And(-x < y,y <
x), 0 < z], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [0, 0], [1, 1]]]], [[
3, 2, 3, 2, 1], [0 < v, u = -(v^2+2)^(1/2), And(-1 < x,x < 1), y = x-1, z = z]
, [regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152], [0, 0], [-1,
-1], [0, 0]]]], [[3, 12, 1, 5, 1], [0 < v, u = (v^2+2)^(1/2), x < -1, 1-x < y,
z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [-2, -2], [
4, 4], [0, 0]]]], [[1, 9, 5, 4, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And
(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/2097152,
479311/2097152], [101115/131072, 808921/1048576], [-2, -2]]]], [[1, 9, 5, 4, 2
], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+
v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576,
1265743/1048576], [479311/2097152, 479311/2097152], [101115/131072, 808921/
1048576], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 5, 4, 3], [v < 0, 
And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, And(
-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [101115/
131072, 808921/1048576], [-1/4194304, -1/4194304]]]], [[1, 9, 5, 4, 4], [v < 0
, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z
= (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [479311/2097152, 479311/2097152], [101115/131072, 808921/1048576], [
193151/262144, 772605/1048576]]]], [[1, 9, 5, 4, 5], [v < 0, And(-v < u,u < (v
^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) <
z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/
2097152, 479311/2097152], [101115/131072, 808921/1048576], [2, 2]]]], [[2, 1,
3, 3, 1], [v = 0, u < -2^(1/2), And(-1 < x,x < 1), And(x-u^2+1 < y,y < u^2-x-1
), z = z], [regular_chain, [[0, 0], [-3, -3], [0, 0], [0, 0], [0, 0]]]], [[3,
4, 7, 2, 1], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y = -x, z < 0], [regular_chain
, [[1, 1], [-1482911/1048576, -741455/524288], [2, 2], [-2, -2], [-1, -1]]]],
[[3, 4, 7, 2, 2], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y = -x, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2, 2], [-2, -2],
[0, 0]]]], [[3, 4, 7, 2, 3], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y = -x, 0 < z]
, [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2, 2], [-2, -2
], [1, 1]]]], [[3, 9, 7, 3, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, 
And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [0, 0], [-2, -2]]]], [[
3, 9, 7, 3, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 <
y,y < x-u^2+v^2+1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [2, 2], [0, 0], [-772605/1048576, -1545209/
2097152]]]], [[3, 9, 7, 3, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, 
And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^
2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2,
2], [0, 0], [-1/4194304, -1/4194304]]]], [[3, 9, 7, 3, 4], [0 < v, And(v < u,u
< (v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1
)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2],
[0, 0], [193151/262144, 772605/1048576]]]], [[3, 9, 7, 3, 5], [0 < v, And(v <
u,u < (v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1
)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2,
2], [0, 0], [2, 2]]]], [[1, 2, 1, 4, 1], [v < 0, u = -(v^2+2)^(1/2), x < -1, y
= 1-x, z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152]
, [-2, -2], [3, 3], [0, 0]]]], [[1, 7, 1, 5, 1], [v < 0, And(v < u,u < -v), x
< u^2-v^2-1, u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [0, 0], [-3, -3], [2, 2], [-3, -3]]]], [[1, 7, 1, 5, 2], [v < 0, And(v <
u,u < -v), x < u^2-v^2-1, u^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-3, -3], [2, 2], [-1482911/1048576, -741455
/524288]]]], [[1, 7, 1, 5, 3], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, u^2-v
^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [-3, -3], [2, 2], [0, 0]]]], [[1, 7, 1, 5, 4
], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, u^2-v^2-x-1 < y, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [2, 2], [741455/524288,
1482911/1048576]]]], [[1, 7, 1, 5, 5], [v < 0, And(v < u,u < -v), x < u^2-v^2-\
1, u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0]
, [-3, -3], [2, 2], [3, 3]]]], [[2, 8, 5, 2, 1], [v = 0, u = 1, And(0 < x,x <
1), y = -x, z < 0], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [-1/2, -1/2],
[-1, -1]]]], [[2, 8, 5, 2, 2], [v = 0, u = 1, And(0 < x,x < 1), y = -x, z = 0]
, [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [-1/2, -1/2], [0, 0]]]], [[2, 8
, 5, 2, 3], [v = 0, u = 1, And(0 < x,x < 1), y = -x, 0 < z], [regular_chain, [
[0, 0], [1, 1], [1/2, 1/2], [-1/2, -1/2], [1, 1]]]], [[3, 2, 3, 1, 1], [0 < v,
u = -(v^2+2)^(1/2), And(-1 < x,x < 1), y < x-1, z = z], [regular_chain, [[1, 1
], [-1816187/1048576, -3632373/2097152], [0, 0], [-2, -2], [0, 0]]]], [[3, 12,
2, 1, 1], [0 < v, u = (v^2+2)^(1/2), x = -1, y < -2, z = z], [regular_chain, [
[1, 1], [908093/524288, 1816187/1048576], [-1, -1], [-3, -3], [0, 0]]]], [[1,
9, 5, 5, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1),
x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743
/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [2, 2], [-2, -2]
]]], [[1, 9, 5, 5, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 <
x,x < 1), x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1]
, [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [2, 2]
, [-772605/1048576, -1545209/2097152]]]], [[1, 9, 5, 5, 3], [v < 0, And(-v < u
,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, And(-(-u^2+v^2
+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [2, 2], [-1/
4194304, -1/4194304]]]], [[1, 9, 5, 5, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2
)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/2097152,
479311/2097152], [2, 2], [193151/262144, 772605/1048576]]]], [[1, 9, 5, 5, 5],
[v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 <
y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [479311/2097152, 479311/2097152], [2, 2], [2, 2]]]], [[2, 1,
3, 4, 1], [v = 0, u < -2^(1/2), And(-1 < x,x < 1), y = u^2-x-1, z = z], [
regular_chain, [[0, 0], [-3, -3], [0, 0], [8, 8], [0, 0]]]], [[3, 4, 7, 1, 1],
[0 < v, u = -(v^2+1)^(1/2), 1 < x, y < -x, z < 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [2, 2], [-3, -3], [-1, -1]]]], [[3, 4, 7, 1,
2], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y < -x, z = 0], [regular_chain, [[1, 1]
, [-1482911/1048576, -741455/524288], [2, 2], [-3, -3], [0, 0]]]], [[3, 4, 7,
1, 3], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y < -x, 0 < z], [regular_chain, [[1,
1], [-1482911/1048576, -741455/524288], [2, 2], [-3, -3], [1, 1]]]], [[3, 9, 7
, 2, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, z < -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576]
, [2, 2], [-5332835/2097152, -2666417/1048576], [-2, -2]]]], [[3, 9, 7, 2, 2],
[0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, z = -(-u^2+v^2+1
)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2],
[-5332835/2097152, -2666417/1048576], [-772605/1048576, -1545209/2097152]]]],
[[3, 9, 7, 2, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1
, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1
], [1265743/1048576, 1265743/1048576], [2, 2], [-5332835/2097152, -2666417/
1048576], [-1/4194304, -1/4194304]]]], [[3, 9, 7, 2, 4], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [-5332835/
2097152, -2666417/1048576], [193151/262144, 772605/1048576]]]], [[3, 9, 7, 2,
5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, (-u^2+v^2+1)
^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2,
2], [-5332835/2097152, -2666417/1048576], [2, 2]]]], [[1, 2, 1, 5, 1], [v < 0,
u = -(v^2+2)^(1/2), x < -1, 1-x < y, z = z], [regular_chain, [[-1, -1], [-\
1816187/1048576, -3632373/2097152], [-2, -2], [4, 4], [0, 0]]]], [[1, 7, 1, 2,
1], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, y = x-u^2+v^2+1, z < -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [-1, -1], [-3, -3]]]],
[[1, 7, 1, 2, 2], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, y = x-u^2+v^2+1, z
= -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [-1, -1],
[-1482911/1048576, -741455/524288]]]], [[1, 7, 1, 2, 3], [v < 0, And(v < u,u <
-v), x < u^2-v^2-1, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2
+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [-1, -1], [0, 0]]]],
[[1, 7, 1, 2, 4], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, y = x-u^2+v^2+1, z
= (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [-1, -1],
[741455/524288, 1482911/1048576]]]], [[1, 7, 1, 2, 5], [v < 0, And(v < u,u < -
v), x < u^2-v^2-1, y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [
[-1, -1], [0, 0], [-3, -3], [-1, -1], [3, 3]]]], [[2, 8, 5, 5, 1], [v = 0, u =
1, And(0 < x,x < 1), x < y, z < 0], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2
], [2, 2], [-1, -1]]]], [[2, 8, 5, 5, 2], [v = 0, u = 1, And(0 < x,x < 1), x <
y, z = 0], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [2, 2], [0, 0]]]], [[2
, 8, 5, 5, 3], [v = 0, u = 1, And(0 < x,x < 1), x < y, 0 < z], [regular_chain,
[[0, 0], [1, 1], [1/2, 1/2], [2, 2], [1, 1]]]], [[3, 2, 2, 5, 1], [0 < v, u =
-(v^2+2)^(1/2), x = -1, 2 < y, z = z], [regular_chain, [[1, 1], [-1816187/
1048576, -3632373/2097152], [-1, -1], [3, 3], [0, 0]]]], [[3, 12, 2, 2, 1], [0
< v, u = (v^2+2)^(1/2), x = -1, y = -2, z = z], [regular_chain, [[1, 1], [
908093/524288, 1816187/1048576], [-1, -1], [-2, -2], [0, 0]]]], [[1, 9, 6, 1,
1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, z < -(-u^2+v^
2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1
, 1], [-3, -3], [-2, -2]]]], [[1, 9, 6, 1, 2], [v < 0, And(-v < u,u < (v^2+1)^
(1/2)), x = 1, y < u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [1265743/1048576, 1265743/1048576], [1, 1], [-3, -3], [-772605/1048576, -\
1545209/2097152]]]], [[1, 9, 6, 1, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x = 1, y < u^2-v^2-2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [-3, -3]
, [-1/4194304, -1/4194304]]]], [[1, 9, 6, 1, 4], [v < 0, And(-v < u,u < (v^2+1
)^(1/2)), x = 1, y < u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [1265743/1048576, 1265743/1048576], [1, 1], [-3, -3], [193151/262144, 
772605/1048576]]]], [[1, 9, 6, 1, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x
= 1, y < u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [1, 1], [-3, -3], [2, 2]]]], [[2, 1, 3, 1,
1], [v = 0, u < -2^(1/2), And(-1 < x,x < 1), y < x-u^2+1, z = z], [
regular_chain, [[0, 0], [-3, -3], [0, 0], [-9, -9], [0, 0]]]], [[3, 4, 7, 4, 1
], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y = x, z < 0], [regular_chain, [[1, 1],
[-1482911/1048576, -741455/524288], [2, 2], [2, 2], [-1, -1]]]], [[3, 4, 7, 4,
2], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y = x, z = 0], [regular_chain, [[1, 1],
[-1482911/1048576, -741455/524288], [2, 2], [2, 2], [0, 0]]]], [[3, 4, 7, 4, 3
], [0 < v, u = -(v^2+1)^(1/2), 1 < x, y = x, 0 < z], [regular_chain, [[1, 1],
[-1482911/1048576, -741455/524288], [2, 2], [2, 2], [1, 1]]]], [[3, 9, 7, 1, 1
], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, y < u^2-v^2-x-1, z < -(-u^2+v^
2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2,
2], [-4, -4], [-2, -2]]]], [[3, 9, 7, 1, 2], [0 < v, And(v < u,u < (v^2+1)^(1/
2)), 1 < x, y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [1265743/1048576, 1265743/1048576], [2, 2], [-4, -4], [-772605/1048576, -\
1545209/2097152]]]], [[3, 9, 7, 1, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1
< x, y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [-4, -4],
[-1/4194304, -1/4194304]]]], [[3, 9, 7, 1, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), 1 < x, y < u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1
], [1265743/1048576, 1265743/1048576], [2, 2], [-4, -4], [193151/262144, 
772605/1048576]]]], [[3, 9, 7, 1, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1
< x, y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [2, 2], [-4, -4], [2, 2]]]], [[1, 2, 2, 1,
1], [v < 0, u = -(v^2+2)^(1/2), x = -1, y < -2, z = z], [regular_chain, [[-1,
-1], [-1816187/1048576, -3632373/2097152], [-1, -1], [-3, -3], [0, 0]]]], [[1,
7, 1, 3, 1], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3
, -3], [0, 0], [-3, -3]]]], [[1, 7, 1, 3, 2], [v < 0, And(v < u,u < -v), x < u
^2-v^2-1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-3, -3], [0, 0], [-1482911/1048576, -741455
/524288]]]], [[1, 7, 1, 3, 3], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, And(x
-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^
(1/2))], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [0, 0], [0, 0]]]], [[1,
7, 1, 3, 4], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3,
-3], [0, 0], [741455/524288, 1482911/1048576]]]], [[1, 7, 1, 3, 5], [v < 0, 
And(v < u,u < -v), x < u^2-v^2-1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), (-u^2+
v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [0, 0], [3, 3]
]]], [[2, 8, 5, 4, 1], [v = 0, u = 1, And(0 < x,x < 1), y = x, z < 0], [
regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [1/2, 1/2], [-1, -1]]]], [[2, 8, 5
, 4, 2], [v = 0, u = 1, And(0 < x,x < 1), y = x, z = 0], [regular_chain, [[0,
0], [1, 1], [1/2, 1/2], [1/2, 1/2], [0, 0]]]], [[2, 8, 5, 4, 3], [v = 0, u = 1
, And(0 < x,x < 1), y = x, 0 < z], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2]
, [1/2, 1/2], [1, 1]]]], [[3, 2, 2, 4, 1], [0 < v, u = -(v^2+2)^(1/2), x = -1,
y = 2, z = z], [regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152],
[-1, -1], [2, 2], [0, 0]]]], [[3, 12, 2, 3, 1], [0 < v, u = (v^2+2)^(1/2), x =
-1, And(-2 < y,y < 2), z = z], [regular_chain, [[1, 1], [908093/524288, 
1816187/1048576], [-1, -1], [0, 0], [0, 0]]]], [[1, 9, 6, 2, 1], [v < 0, And(-
v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [-\
3235683/2097152, -1617841/1048576], [-2, -2]]]], [[1, 9, 6, 2, 2], [v < 0, And
(-v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [-\
3235683/2097152, -1617841/1048576], [-772605/1048576, -1545209/2097152]]]], [[
1, 9, 6, 2, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, 
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [1265743/1048576, 1265743/1048576], [1, 1], [-3235683/2097152, -1617841/
1048576], [-1/4194304, -1/4194304]]]], [[1, 9, 6, 2, 4], [v < 0, And(-v < u,u
< (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [-\
3235683/2097152, -1617841/1048576], [193151/262144, 772605/1048576]]]], [[1, 9
, 6, 2, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, (-u^2
+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [1, 1], [-3235683/2097152, -1617841/1048576], [2, 2]]]], [[2, 1, 3,
2, 1], [v = 0, u < -2^(1/2), And(-1 < x,x < 1), y = x-u^2+1, z = z], [
regular_chain, [[0, 0], [-3, -3], [0, 0], [-8, -8], [0, 0]]]], [[3, 4, 7, 3, 1
], [0 < v, u = -(v^2+1)^(1/2), 1 < x, And(-x < y,y < x), z < 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2, 2], [0, 0], [-\
1, -1]]]], [[3, 4, 7, 3, 2], [0 < v, u = -(v^2+1)^(1/2), 1 < x, And(-x < y,y <
x), z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2, 2
], [0, 0], [0, 0]]]], [[3, 4, 7, 3, 3], [0 < v, u = -(v^2+1)^(1/2), 1 < x, And
(-x < y,y < x), 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/
524288], [2, 2], [0, 0], [1, 1]]]], [[3, 9, 6, 5, 1], [0 < v, And(v < u,u < (v
^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [3, 3], [-2, -2]]]], [[3,
9, 6, 5, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [1, 1], [3, 3], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 6, 5
, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, And(-(-u^2+
v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [1, 1], [3, 3], [-1/4194304, -1/4194304]]]], [[3, 9
, 6, 5, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, z = (
-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576
], [1, 1], [3, 3], [193151/262144, 772605/1048576]]]], [[3, 9, 6, 5, 5], [0 <
v, And(v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, (-u^2+v^2+1)^(1/2) < z
], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [3, 3]
, [2, 2]]]], [[1, 9, 6, 3, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, 
And(u^2-v^2-2 < y,y < -u^2+v^2+2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [0, 0], [-2, -2]]]], [[1
, 9, 6, 3, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y
,y < -u^2+v^2+2), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [1, 1], [0, 0], [-772605/1048576, -1545209/
2097152]]]], [[1, 9, 6, 3, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, 
And(u^2-v^2-2 < y,y < -u^2+v^2+2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1
)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1,
1], [0, 0], [-1/4194304, -1/4194304]]]], [[1, 9, 6, 3, 4], [v < 0, And(-v < u,
u < (v^2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1]
, [0, 0], [193151/262144, 772605/1048576]]]], [[1, 9, 6, 3, 5], [v < 0, And(-v
< u,u < (v^2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), (-u^2+v^2+1)
^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1
, 1], [0, 0], [2, 2]]]], [[2, 1, 4, 2, 1], [v = 0, u < -2^(1/2), x = 1, y = -u
^2+2, z = z], [regular_chain, [[0, 0], [-3, -3], [1, 1], [-7, -7], [0, 0]]]],
[[3, 5, 1, 1, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y < x-u^2+v^
2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [-2, -2], [-3, -3], [-2, -2]]]], [[3, 5, 1, 1, 2], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y < x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/
2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-2, -2],
[-3, -3], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 1, 1, 3], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/
2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [-2, -2], [-3, -3], [-1/4194304, -1/4194304]]]], [[3, 5, 1,
1, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y < x-u^2+v^2+1, z = (-
u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [-3, -3], [193151/262144, 772605/1048576]]]], [[3, 5, 1, 1
, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y < x-u^2+v^2+1, (-u^2+v
^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576
], [-2, -2], [-3, -3], [2, 2]]]], [[3, 10, 1, 2, 1], [0 < v, u = (v^2+1)^(1/2)
, x < -1, y = x, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/
1048576], [-2, -2], [-2, -2], [-1, -1]]]], [[3, 10, 1, 2, 2], [0 < v, u = (v^2
+1)^(1/2), x < -1, y = x, z = 0], [regular_chain, [[1, 1], [741455/524288, 
1482911/1048576], [-2, -2], [-2, -2], [0, 0]]]], [[3, 10, 1, 2, 3], [0 < v, u
= (v^2+1)^(1/2), x < -1, y = x, 0 < z], [regular_chain, [[1, 1], [741455/
524288, 1482911/1048576], [-2, -2], [-2, -2], [1, 1]]]], [[1, 1, 7, 4, 1], [v
< 0, u < -(v^2+2)^(1/2), u^2-v^2-1 < x, y = x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [-3, -3], [8, 8], [1, 1], [0, 0]]]], [[1, 6, 5, 5, 1
], [v < 0, u = v, 1 < x, x+1 < y, z < -1], [regular_chain, [[-1, -1], [-1, -1]
, [2, 2], [4, 4], [-2, -2]]]], [[1, 6, 5, 5, 2], [v < 0, u = v, 1 < x, x+1 < y
, z = -1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [4, 4], [-1, -1]]]], [
[1, 6, 5, 5, 3], [v < 0, u = v, 1 < x, x+1 < y, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [2, 2], [4, 4], [0, 0]]]], [[1, 6, 5, 5, 4
], [v < 0, u = v, 1 < x, x+1 < y, z = 1], [regular_chain, [[-1, -1], [-1, -1],
[2, 2], [4, 4], [1, 1]]]], [[1, 6, 5, 5, 5], [v < 0, u = v, 1 < x, x+1 < y, 1
< z], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [4, 4], [2, 2]]]], [[2, 8,
4, 2, 1], [v = 0, u = 1, x = 0, y = 0, z < 0], [regular_chain, [[0, 0], [1, 1]
, [0, 0], [0, 0], [-1, -1]]]], [[2, 8, 4, 2, 2], [v = 0, u = 1, x = 0, y = 0,
z = 0], [regular_chain, [[0, 0], [1, 1], [0, 0], [0, 0], [0, 0]]]], [[2, 8, 4,
2, 3], [v = 0, u = 1, x = 0, y = 0, 0 < z], [regular_chain, [[0, 0], [1, 1], [
0, 0], [0, 0], [1, 1]]]], [[3, 2, 2, 3, 1], [0 < v, u = -(v^2+2)^(1/2), x = -1
, And(-2 < y,y < 2), z = z], [regular_chain, [[1, 1], [-1816187/1048576, -\
3632373/2097152], [-1, -1], [0, 0], [0, 0]]]], [[3, 12, 1, 1, 1], [0 < v, u =
(v^2+2)^(1/2), x < -1, y < x-1, z = z], [regular_chain, [[1, 1], [908093/
524288, 1816187/1048576], [-2, -2], [-4, -4], [0, 0]]]], [[1, 9, 6, 4, 1], [v
< 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, z < -(-u^2+v^2+1)^(
1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1],
[1617841/1048576, 808921/524288], [-2, -2]]]], [[1, 9, 6, 4, 2], [v < 0, And(-
v < u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [1617841
/1048576, 808921/524288], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 6, 4
, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, And(-(-u^2
+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [1, 1], [1617841/1048576, 808921/524288], [
-1/4194304, -1/4194304]]]], [[1, 9, 6, 4, 4], [v < 0, And(-v < u,u < (v^2+1)^(
1/2)), x = 1, y = -u^2+v^2+2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -\
1], [1265743/1048576, 1265743/1048576], [1, 1], [1617841/1048576, 808921/
524288], [193151/262144, 772605/1048576]]]], [[1, 9, 6, 4, 5], [v < 0, And(-v
< u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [1617841
/1048576, 808921/524288], [2, 2]]]], [[2, 1, 4, 3, 1], [v = 0, u < -2^(1/2), x
= 1, And(-u^2+2 < y,y < u^2-2), z = z], [regular_chain, [[0, 0], [-3, -3], [1,
1], [0, 0], [0, 0]]]], [[3, 4, 7, 5, 1], [0 < v, u = -(v^2+1)^(1/2), 1 < x, x
< y, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2,
2], [3, 3], [-1, -1]]]], [[3, 4, 7, 5, 2], [0 < v, u = -(v^2+1)^(1/2), 1 < x,
x < y, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2
, 2], [3, 3], [0, 0]]]], [[3, 4, 7, 5, 3], [0 < v, u = -(v^2+1)^(1/2), 1 < x,
x < y, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [2
, 2], [3, 3], [1, 1]]]], [[3, 10, 1, 1, 1], [0 < v, u = (v^2+1)^(1/2), x < -1,
y < x, z < 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576], [-2,
-2], [-3, -3], [-1, -1]]]], [[3, 10, 1, 1, 2], [0 < v, u = (v^2+1)^(1/2), x <
-1, y < x, z = 0], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576],
[-2, -2], [-3, -3], [0, 0]]]], [[3, 10, 1, 1, 3], [0 < v, u = (v^2+1)^(1/2), x
< -1, y < x, 0 < z], [regular_chain, [[1, 1], [741455/524288, 1482911/1048576]
, [-2, -2], [-3, -3], [1, 1]]]], [[1, 1, 7, 5, 1], [v < 0, u < -(v^2+2)^(1/2),
u^2-v^2-1 < x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[-1, -1], [-3, -3], [
8, 8], [2, 2], [0, 0]]]], [[1, 7, 1, 1, 1], [v < 0, And(v < u,u < -v), x < u^2
-v^2-1, y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1],
[0, 0], [-3, -3], [-2, -2], [-3, -3]]]], [[1, 7, 1, 1, 2], [v < 0, And(v < u,u
< -v), x < u^2-v^2-1, y < x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-3, -3], [-2, -2], [-1482911/1048576, -\
741455/524288]]]], [[1, 7, 1, 1, 3], [v < 0, And(v < u,u < -v), x < u^2-v^2-1,
y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [-3, -3], [-2, -2], [0, 0]]]], [[1, 7, 1, 1,
4], [v < 0, And(v < u,u < -v), x < u^2-v^2-1, y < x-u^2+v^2+1, z = (-u^2+v^2+1
)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3, -3], [-2, -2], [741455/
524288, 1482911/1048576]]]], [[1, 7, 1, 1, 5], [v < 0, And(v < u,u < -v), x <
u^2-v^2-1, y < x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1]
, [0, 0], [-3, -3], [-2, -2], [3, 3]]]], [[2, 8, 4, 1, 1], [v = 0, u = 1, x =
0, y < 0, z < 0], [regular_chain, [[0, 0], [1, 1], [0, 0], [-1, -1], [-1, -1]]
]], [[2, 8, 4, 1, 2], [v = 0, u = 1, x = 0, y < 0, z = 0], [regular_chain, [[0
, 0], [1, 1], [0, 0], [-1, -1], [0, 0]]]], [[2, 8, 4, 1, 3], [v = 0, u = 1, x
= 0, y < 0, 0 < z], [regular_chain, [[0, 0], [1, 1], [0, 0], [-1, -1], [1, 1]]
]], [[3, 2, 2, 2, 1], [0 < v, u = -(v^2+2)^(1/2), x = -1, y = -2, z = z], [
regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152], [-1, -1], [-2, -\
2], [0, 0]]]], [[3, 12, 1, 2, 1], [0 < v, u = (v^2+2)^(1/2), x < -1, y = x-1,
z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [-2, -2], [
-3, -3], [0, 0]]]], [[1, 9, 6, 5, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x
= 1, -u^2+v^2+2 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [1, 1], [3, 3], [-2, -2]]]], [[1, 9, 6, 5,
2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, z = -(-u^2+v
^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [
1, 1], [3, 3], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 6, 5, 3], [v <
0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, And(-(-u^2+v^2+1)^(1/
2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576,
1265743/1048576], [1, 1], [3, 3], [-1/4194304, -1/4194304]]]], [[1, 9, 6, 5, 4
], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, z = (-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1,
1], [3, 3], [193151/262144, 772605/1048576]]]], [[1, 9, 6, 5, 5], [v < 0, And(
-v < u,u < (v^2+1)^(1/2)), x = 1, -u^2+v^2+2 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [1, 1], [3, 3],
[2, 2]]]], [[2, 1, 3, 5, 1], [v = 0, u < -2^(1/2), And(-1 < x,x < 1), u^2-x-1
< y, z = z], [regular_chain, [[0, 0], [-3, -3], [0, 0], [9, 9], [0, 0]]]], [[3
, 5, 1, 3, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, And(x-u^2+v^2+1
< y,y < u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [-2, -2], [0, 0], [-2, -2]]]], [[3, 5, 1,
3, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [0, 0], [-772605/1048576, -1545209/
2097152]]]], [[3, 5, 1, 3, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1,
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^
2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
-2, -2], [0, 0], [-1/4194304, -1/4194304]]]], [[3, 5, 1, 3, 4], [0 < v, And(-(
v^2+1)^(1/2) < u,u < -v), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = (-
u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [0, 0], [193151/262144, 772605/1048576]]]], [[3, 5, 1, 3,
5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, And(x-u^2+v^2+1 < y,y < u^
2-v^2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [0, 0], [2, 2]]]], [[3, 9, 7, 5, 1], [0
< v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(
1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [4
, 4], [-2, -2]]]], [[3, 9, 7, 5, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 <
x, x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [2, 2], [4, 4], [-772605/1048576, -1545209/
2097152]]]], [[3, 9, 7, 5, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, x-
u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [4, 4], [-\
1/4194304, -1/4194304]]]], [[3, 9, 7, 5, 4], [0 < v, And(v < u,u < (v^2+1)^(1/
2)), 1 < x, x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [2, 2], [4, 4], [193151/262144, 772605/
1048576]]]], [[3, 9, 7, 5, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, x-
u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [2, 2], [4, 4], [2, 2]]]], [[1, 2, 1, 1, 1], [v < 0
, u = -(v^2+2)^(1/2), x < -1, y < x-1, z = z], [regular_chain, [[-1, -1], [-\
1816187/1048576, -3632373/2097152], [-2, -2], [-4, -4], [0, 0]]]], [[1, 6, 5,
3, 1], [v < 0, u = v, 1 < x, And(-1-x < y,y < x+1), z < -1], [regular_chain, [
[-1, -1], [-1, -1], [2, 2], [0, 0], [-2, -2]]]], [[1, 6, 5, 3, 2], [v < 0, u =
v, 1 < x, And(-1-x < y,y < x+1), z = -1], [regular_chain, [[-1, -1], [-1, -1],
[2, 2], [0, 0], [-1, -1]]]], [[1, 6, 5, 3, 3], [v < 0, u = v, 1 < x, And(-1-x
< y,y < x+1), And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [2, 2],
[0, 0], [0, 0]]]], [[1, 6, 5, 3, 4], [v < 0, u = v, 1 < x, And(-1-x < y,y < x+
1), z = 1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [0, 0], [1, 1]]]], [[
1, 6, 5, 3, 5], [v < 0, u = v, 1 < x, And(-1-x < y,y < x+1), 1 < z], [
regular_chain, [[-1, -1], [-1, -1], [2, 2], [0, 0], [2, 2]]]], [[2, 8, 5, 1, 1
], [v = 0, u = 1, And(0 < x,x < 1), y < -x, z < 0], [regular_chain, [[0, 0], [
1, 1], [1/2, 1/2], [-2, -2], [-1, -1]]]], [[2, 8, 5, 1, 2], [v = 0, u = 1, And
(0 < x,x < 1), y < -x, z = 0], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [-\
2, -2], [0, 0]]]], [[2, 8, 5, 1, 3], [v = 0, u = 1, And(0 < x,x < 1), y < -x,
0 < z], [regular_chain, [[0, 0], [1, 1], [1/2, 1/2], [-2, -2], [1, 1]]]], [[3,
2, 2, 1, 1], [0 < v, u = -(v^2+2)^(1/2), x = -1, y < -2, z = z], [
regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152], [-1, -1], [-3, -\
3], [0, 0]]]], [[3, 12, 1, 3, 1], [0 < v, u = (v^2+2)^(1/2), x < -1, And(x-1 <
y,y < 1-x), z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576],
[-2, -2], [0, 0], [0, 0]]]], [[1, 9, 7, 1, 1], [v < 0, And(-v < u,u < (v^2+1)^
(1/2)), 1 < x, y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1
, -1], [1265743/1048576, 1265743/1048576], [2, 2], [-4, -4], [-2, -2]]]], [[1,
9, 7, 1, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y < u^2-v^2-x-1, z
= -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [2, 2], [-4, -4], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 7,
1, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y < u^2-v^2-x-1, And(-(-u
^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [2, 2], [-4, -4], [-1/4194304, -1/4194304]]
]], [[1, 9, 7, 1, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y < u^2-v^
2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [2, 2], [-4, -4], [193151/262144, 772605/1048576]]]], [[1, 9
, 7, 1, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y < u^2-v^2-x-1, (-u
^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [2, 2], [-4, -4], [2, 2]]]], [[2, 1, 4, 1, 1], [v = 0, u < -2^(1/2),
x = 1, y < -u^2+2, z = z], [regular_chain, [[0, 0], [-3, -3], [1, 1], [-8, -8]
, [0, 0]]]], [[3, 5, 1, 2, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1,
y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [-1527887/1048576, -763943/524288], [-2,
-2]]]], [[3, 5, 1, 2, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y =
x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [-1527887/1048576, -763943/524288], [-\
772605/1048576, -1545209/2097152]]]], [[3, 5, 1, 2, 3], [0 < v, And(-(v^2+1)^(
1/2) < u,u < -v), x < -1, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u
^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [-1527887/1048576, -763943/524288], [-1/4194304, -1/
4194304]]]], [[3, 5, 1, 2, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1,
y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [-1527887/1048576, -763943/524288], [
193151/262144, 772605/1048576]]]], [[3, 5, 1, 2, 5], [0 < v, And(-(v^2+1)^(1/2
) < u,u < -v), x < -1, y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-2, -2], [-\
1527887/1048576, -763943/524288], [2, 2]]]], [[3, 9, 7, 4, 1], [0 < v, And(v <
u,u < (v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [2666417/
1048576, 1333209/524288], [-2, -2]]]], [[3, 9, 7, 4, 2], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [2666417/
1048576, 1333209/524288], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 7, 4
, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, And(-(-u^2
+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [2, 2], [2666417/1048576, 1333209/524288], [-1/
4194304, -1/4194304]]]], [[3, 9, 7, 4, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)
), 1 < x, y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [2, 2], [2666417/1048576, 1333209/524288],
[193151/262144, 772605/1048576]]]], [[3, 9, 7, 4, 5], [0 < v, And(v < u,u < (v
^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[1, 1], [1265743/1048576, 1265743/1048576], [2, 2], [2666417/1048576, 1333209
/524288], [2, 2]]]], [[1, 2, 1, 2, 1], [v < 0, u = -(v^2+2)^(1/2), x < -1, y =
x-1, z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152],
[-2, -2], [-3, -3], [0, 0]]]], [[1, 6, 5, 4, 1], [v < 0, u = v, 1 < x, y = x+1
, z < -1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [3, 3], [-2, -2]]]], [
[1, 6, 5, 4, 2], [v < 0, u = v, 1 < x, y = x+1, z = -1], [regular_chain, [[-1,
-1], [-1, -1], [2, 2], [3, 3], [-1, -1]]]], [[1, 6, 5, 4, 3], [v < 0, u = v, 1
< x, y = x+1, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [2, 2],
[3, 3], [0, 0]]]], [[1, 6, 5, 4, 4], [v < 0, u = v, 1 < x, y = x+1, z = 1], [
regular_chain, [[-1, -1], [-1, -1], [2, 2], [3, 3], [1, 1]]]], [[1, 6, 5, 4, 5
], [v < 0, u = v, 1 < x, y = x+1, 1 < z], [regular_chain, [[-1, -1], [-1, -1],
[2, 2], [3, 3], [2, 2]]]], [[2, 8, 4, 3, 1], [v = 0, u = 1, x = 0, 0 < y, z <
0], [regular_chain, [[0, 0], [1, 1], [0, 0], [1, 1], [-1, -1]]]], [[2, 8, 4, 3
, 2], [v = 0, u = 1, x = 0, 0 < y, z = 0], [regular_chain, [[0, 0], [1, 1], [0
, 0], [1, 1], [0, 0]]]], [[2, 8, 4, 3, 3], [v = 0, u = 1, x = 0, 0 < y, 0 < z]
, [regular_chain, [[0, 0], [1, 1], [0, 0], [1, 1], [1, 1]]]], [[3, 2, 1, 5, 1]
, [0 < v, u = -(v^2+2)^(1/2), x < -1, 1-x < y, z = z], [regular_chain, [[1, 1]
, [-1816187/1048576, -3632373/2097152], [-2, -2], [4, 4], [0, 0]]]], [[3, 12,
1, 4, 1], [0 < v, u = (v^2+2)^(1/2), x < -1, y = 1-x, z = z], [regular_chain,
[[1, 1], [908093/524288, 1816187/1048576], [-2, -2], [3, 3], [0, 0]]]], [[1, 2
, 3, 2, 1], [v < 0, u = -(v^2+2)^(1/2), And(-1 < x,x < 1), y = x-1, z = z], [
regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [0, 0], [-1, -\
1], [0, 0]]]], [[1, 7, 3, 5, 1], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,
x < -1), x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1],
[0, 0], [-3/2, -3/2], [2, 2], [-3, -3]]]], [[1, 7, 3, 5, 2], [v < 0, And(v < u
,u < -v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [2, 2], [-1482911/1048576,
-741455/524288]]]], [[1, 7, 3, 5, 3], [v < 0, And(v < u,u < -v), And(u^2-v^2-1
< x,x < -1), x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/
2))], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [2, 2], [0, 0]]]], [[1,
7, 3, 5, 4], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1
< y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2],
[2, 2], [741455/524288, 1482911/1048576]]]], [[1, 7, 3, 5, 5], [v < 0, And(v <
u,u < -v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z]
, [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [2, 2], [3, 3]]]], [[2, 8,
3, 2, 1], [v = 0, u = 1, And(-1 < x,x < 0), y = x, z < 0], [regular_chain, [[0
, 0], [1, 1], [-1/2, -1/2], [-1/2, -1/2], [-1, -1]]]], [[2, 8, 3, 2, 2], [v =
0, u = 1, And(-1 < x,x < 0), y = x, z = 0], [regular_chain, [[0, 0], [1, 1], [
-1/2, -1/2], [-1/2, -1/2], [0, 0]]]], [[2, 8, 3, 2, 3], [v = 0, u = 1, And(-1
< x,x < 0), y = x, 0 < z], [regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [-1/
2, -1/2], [1, 1]]]], [[3, 2, 1, 3, 1], [0 < v, u = -(v^2+2)^(1/2), x < -1, And
(x-1 < y,y < 1-x), z = z], [regular_chain, [[1, 1], [-1816187/1048576, -\
3632373/2097152], [-2, -2], [0, 0], [0, 0]]]], [[3, 12, 3, 4, 1], [0 < v, u =
(v^2+2)^(1/2), And(-1 < x,x < 1), y = 1-x, z = z], [regular_chain, [[1, 1], [
908093/524288, 1816187/1048576], [0, 0], [1, 1], [0, 0]]]], [[1, 9, 7, 3, 1],
[v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^
2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [2, 2], [0, 0], [-2, -2]]]], [[1, 9, 7, 3, 2], [v < 0, And(-
v < u,u < (v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [2, 2], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 7, 3
, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-
u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [0, 0],
[-1/4194304, -1/4194304]]]], [[1, 9, 7, 3, 4], [v < 0, And(-v < u,u < (v^2+1)^
(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [0, 0],
[193151/262144, 772605/1048576]]]], [[1, 9, 7, 3, 5], [v < 0, And(-v < u,u < (
v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2)
< z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [
0, 0], [2, 2]]]], [[2, 1, 5, 2, 1], [v = 0, u < -2^(1/2), And(1 < x,x < u^2-1)
, y = x-u^2+1, z = z], [regular_chain, [[0, 0], [-3, -3], [9/2, 9/2], [-7/2, -\
7/2], [0, 0]]]], [[3, 4, 5, 3, 1], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x < 1
), And(-x < y,y < x), z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [1/2, 1/2], [0, 0], [-1, -1]]]], [[3, 4, 5, 3, 2], [0 < v, u =
-(v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y < x), z = 0], [regular_chain, [
[1, 1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [0, 0], [0, 0]]]], [[3
, 4, 5, 3, 3], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y < x)
, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1/2, 1
/2], [0, 0], [1, 1]]]], [[3, 9, 5, 4, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2))
, And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 
479311/2097152], [101115/131072, 808921/1048576], [-2, -2]]]], [[3, 9, 5, 4, 2
], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v
^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [479311/2097152, 479311/2097152], [101115/131072, 808921/
1048576], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 5, 4, 3], [0 < v, 
And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, And(-
(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [101115/
131072, 808921/1048576], [-1/4194304, -1/4194304]]]], [[3, 9, 5, 4, 4], [0 < v
, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [479311/2097152, 479311/2097152], [101115/131072, 808921/1048576], [
193151/262144, 772605/1048576]]]], [[3, 9, 5, 4, 5], [0 < v, And(v < u,u < (v^
2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z
], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/
2097152, 479311/2097152], [101115/131072, 808921/1048576], [2, 2]]]], [[1, 2,
3, 1, 1], [v < 0, u = -(v^2+2)^(1/2), And(-1 < x,x < 1), y < x-1, z = z], [
regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [0, 0], [-2, -\
2], [0, 0]]]], [[1, 7, 3, 4, 1], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,
x < -1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1],
[0, 0], [-3/2, -3/2], [1/2, 1/2], [-3, -3]]]], [[1, 7, 3, 4, 2], [v < 0, And(v
< u,u < -v), And(u^2-v^2-1 < x,x < -1), y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/
2)], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [1/2, 1/2], [-1482911/
1048576, -741455/524288]]]], [[1, 7, 3, 4, 3], [v < 0, And(v < u,u < -v), And(
u^2-v^2-1 < x,x < -1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+
v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [1/2, 1/2], [
0, 0]]]], [[1, 7, 3, 4, 4], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -\
1), y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0
], [-3/2, -3/2], [1/2, 1/2], [741455/524288, 1482911/1048576]]]], [[1, 7, 3, 4
, 5], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), y = x-u^2+v^2+1, (
-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [1/2,
1/2], [3, 3]]]], [[2, 8, 3, 3, 1], [v = 0, u = 1, And(-1 < x,x < 0), And(x < y
,y < -x), z < 0], [regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [0, 0], [-1,
-1]]]], [[2, 8, 3, 3, 2], [v = 0, u = 1, And(-1 < x,x < 0), And(x < y,y < -x),
z = 0], [regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [0, 0], [0, 0]]]], [[2,
8, 3, 3, 3], [v = 0, u = 1, And(-1 < x,x < 0), And(x < y,y < -x), 0 < z], [
regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [0, 0], [1, 1]]]], [[3, 2, 1, 4,
1], [0 < v, u = -(v^2+2)^(1/2), x < -1, y = 1-x, z = z], [regular_chain, [[1,
1], [-1816187/1048576, -3632373/2097152], [-2, -2], [3, 3], [0, 0]]]], [[3, 12
, 3, 3, 1], [0 < v, u = (v^2+2)^(1/2), And(-1 < x,x < 1), And(x-1 < y,y < 1-x)
, z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [0, 0], [
0, 0], [0, 0]]]], [[1, 9, 7, 2, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 <
x, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [2, 2], [-5332835/2097152, -2666417/1048576
], [-2, -2]]]], [[1, 9, 7, 2, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x
, y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [2, 2], [-5332835/2097152, -2666417/1048576
], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 7, 2, 3], [v < 0, And(-v <
u,u < (v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [2, 2], [-5332835/2097152, -2666417/1048576], [-1/4194304, -1/
4194304]]]], [[1, 9, 7, 2, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y
= u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [2, 2], [-5332835/2097152, -2666417/1048576], [
193151/262144, 772605/1048576]]]], [[1, 9, 7, 2, 5], [v < 0, And(-v < u,u < (v
^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [-5332835/2097152, -\
2666417/1048576], [2, 2]]]], [[2, 1, 5, 1, 1], [v = 0, u < -2^(1/2), And(1 < x
,x < u^2-1), y < x-u^2+1, z = z], [regular_chain, [[0, 0], [-3, -3], [9/2, 9/2
], [-5, -5], [0, 0]]]], [[3, 4, 5, 4, 1], [0 < v, u = -(v^2+1)^(1/2), And(0 <
x,x < 1), y = x, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/
524288], [1/2, 1/2], [1/2, 1/2], [-1, -1]]]], [[3, 4, 5, 4, 2], [0 < v, u = -(
v^2+1)^(1/2), And(0 < x,x < 1), y = x, z = 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [1/2, 1/2], [1/2, 1/2], [0, 0]]]], [[3, 4, 5
, 4, 3], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y = x, 0 < z], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [1/2,
1/2], [1, 1]]]], [[3, 9, 5, 5, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u
^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152
], [2, 2], [-2, -2]]]], [[3, 9, 5, 5, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2))
, And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 
479311/2097152], [2, 2], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 5, 5,
3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+
1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [
[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152],
[2, 2], [-1/4194304, -1/4194304]]]], [[3, 9, 5, 5, 4], [0 < v, And(v < u,u < (
v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/
2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/
2097152, 479311/2097152], [2, 2], [193151/262144, 772605/1048576]]]], [[3, 9,
5, 5, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^
2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [2, 2], [2, 2]]]]
, [[1, 2, 3, 4, 1], [v < 0, u = -(v^2+2)^(1/2), And(-1 < x,x < 1), y = 1-x, z
= z], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [0, 0],
[1, 1], [0, 0]]]], [[1, 7, 3, 3, 1], [v < 0, And(v < u,u < -v), And(u^2-v^2-1
< x,x < -1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [0, 0], [-3, -3]]]], [[1, 7, 3
, 3, 2], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1
< y,y < x-u^2+v^2+1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0,
0], [-3/2, -3/2], [0, 0], [-1482911/1048576, -741455/524288]]]], [[1, 7, 3, 3,
3], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1 < y,
y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [0, 0], [0, 0]]]], [[1, 7, 3,
3, 4], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1 <
y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0]
, [-3/2, -3/2], [0, 0], [741455/524288, 1482911/1048576]]]], [[1, 7, 3, 3, 5],
[v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1 < y,y <
x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-3/
2, -3/2], [0, 0], [3, 3]]]], [[2, 8, 3, 4, 1], [v = 0, u = 1, And(-1 < x,x < 0
), y = -x, z < 0], [regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [1/2, 1/2],
[-1, -1]]]], [[2, 8, 3, 4, 2], [v = 0, u = 1, And(-1 < x,x < 0), y = -x, z = 0
], [regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [1/2, 1/2], [0, 0]]]], [[2,
8, 3, 4, 3], [v = 0, u = 1, And(-1 < x,x < 0), y = -x, 0 < z], [regular_chain,
[[0, 0], [1, 1], [-1/2, -1/2], [1/2, 1/2], [1, 1]]]], [[3, 2, 1, 1, 1], [0 < v
, u = -(v^2+2)^(1/2), x < -1, y < x-1, z = z], [regular_chain, [[1, 1], [-\
1816187/1048576, -3632373/2097152], [-2, -2], [-4, -4], [0, 0]]]], [[3, 12, 4,
1, 1], [0 < v, u = (v^2+2)^(1/2), x = 1, y < 0, z = z], [regular_chain, [[1, 1
], [908093/524288, 1816187/1048576], [1, 1], [-1, -1], [0, 0]]]], [[1, 9, 7, 5
, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, x-u^2+v^2+1 < y, z < -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576]
, [2, 2], [4, 4], [-2, -2]]]], [[1, 9, 7, 5, 2], [v < 0, And(-v < u,u < (v^2+1
)^(1/2)), 1 < x, x-u^2+v^2+1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [4, 4], [-772605/1048576,
-1545209/2097152]]]], [[1, 9, 7, 5, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
1 < x, x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))],
[regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [4, 4],
[-1/4194304, -1/4194304]]]], [[1, 9, 7, 5, 4], [v < 0, And(-v < u,u < (v^2+1)^
(1/2)), 1 < x, x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [1265743/1048576, 1265743/1048576], [2, 2], [4, 4], [193151/262144, 
772605/1048576]]]], [[1, 9, 7, 5, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1
< x, x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [2, 2], [4, 4], [2, 2]]]], [[2, 1, 4, 5, 1]
, [v = 0, u < -2^(1/2), x = 1, u^2-2 < y, z = z], [regular_chain, [[0, 0], [-3
, -3], [1, 1], [8, 8], [0, 0]]]], [[3, 4, 5, 5, 1], [0 < v, u = -(v^2+1)^(1/2)
, And(0 < x,x < 1), x < y, z < 0], [regular_chain, [[1, 1], [-1482911/1048576,
-741455/524288], [1/2, 1/2], [2, 2], [-1, -1]]]], [[3, 4, 5, 5, 2], [0 < v, u
= -(v^2+1)^(1/2), And(0 < x,x < 1), x < y, z = 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [1/2, 1/2], [2, 2], [0, 0]]]], [[3, 4, 5, 5,
3], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x < 1), x < y, 0 < z], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [2, 2]
, [1, 1]]]], [[3, 9, 5, 2, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v
^2-1 < x,x < 1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [
-808921/1048576, -3235683/4194304], [-2, -2]]]], [[3, 9, 5, 2, 2], [0 < v, And
(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = -(-u
^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576],
[479311/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304], [-\
772605/1048576, -1545209/2097152]]]], [[3, 9, 5, 2, 3], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(
1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576,
1265743/1048576], [479311/2097152, 479311/2097152], [-808921/1048576, -3235683
/4194304], [-1/4194304, -1/4194304]]]], [[3, 9, 5, 2, 4], [0 < v, And(v < u,u
< (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)^
(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/
2097152, 479311/2097152], [-808921/1048576, -3235683/4194304], [193151/262144,
772605/1048576]]]], [[3, 9, 5, 2, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 
And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 
479311/2097152], [-808921/1048576, -3235683/4194304], [2, 2]]]], [[1, 2, 3, 3,
1], [v < 0, u = -(v^2+2)^(1/2), And(-1 < x,x < 1), And(x-1 < y,y < 1-x), z = z
], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [0, 0], [0
, 0], [0, 0]]]], [[1, 7, 3, 2, 1], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 <
x,x < -1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1
], [0, 0], [-3/2, -3/2], [-1/2, -1/2], [-3, -3]]]], [[1, 7, 3, 2, 2], [v < 0,
And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), y = u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [-1/2, -1/2], [-\
1482911/1048576, -741455/524288]]]], [[1, 7, 3, 2, 3], [v < 0, And(v < u,u < -
v), And(u^2-v^2-1 < x,x < -1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z
< (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [-1/2
, -1/2], [0, 0]]]], [[1, 7, 3, 2, 4], [v < 0, And(v < u,u < -v), And(u^2-v^2-1
< x,x < -1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -\
1], [0, 0], [-3/2, -3/2], [-1/2, -1/2], [741455/524288, 1482911/1048576]]]], [
[1, 7, 3, 2, 5], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), y = u^2
-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-3/2, -\
3/2], [-1/2, -1/2], [3, 3]]]], [[2, 8, 3, 5, 1], [v = 0, u = 1, And(-1 < x,x <
0), -x < y, z < 0], [regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [2, 2], [-1
, -1]]]], [[2, 8, 3, 5, 2], [v = 0, u = 1, And(-1 < x,x < 0), -x < y, z = 0],
[regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [2, 2], [0, 0]]]], [[2, 8, 3, 5
, 3], [v = 0, u = 1, And(-1 < x,x < 0), -x < y, 0 < z], [regular_chain, [[0, 0
], [1, 1], [-1/2, -1/2], [2, 2], [1, 1]]]], [[3, 2, 1, 2, 1], [0 < v, u = -(v^
2+2)^(1/2), x < -1, y = x-1, z = z], [regular_chain, [[1, 1], [-1816187/
1048576, -3632373/2097152], [-2, -2], [-3, -3], [0, 0]]]], [[3, 12, 3, 5, 1],
[0 < v, u = (v^2+2)^(1/2), And(-1 < x,x < 1), 1-x < y, z = z], [regular_chain,
[[1, 1], [908093/524288, 1816187/1048576], [0, 0], [2, 2], [0, 0]]]], [[1, 9,
7, 4, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, z < -
(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [2, 2], [2666417/1048576, 1333209/524288], [-2, -2]]]], [[1, 9, 7, 4
, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, z = -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576]
, [2, 2], [2666417/1048576, 1333209/524288], [-772605/1048576, -1545209/
2097152]]]], [[1, 9, 7, 4, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y
= x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [2666417
/1048576, 1333209/524288], [-1/4194304, -1/4194304]]]], [[1, 9, 7, 4, 4], [v <
0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/
2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [2, 2], [
2666417/1048576, 1333209/524288], [193151/262144, 772605/1048576]]]], [[1, 9,
7, 4, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1, (-u^2
+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [2, 2], [2666417/1048576, 1333209/524288], [2, 2]]]], [[2, 1, 4, 4,
1], [v = 0, u < -2^(1/2), x = 1, y = u^2-2, z = z], [regular_chain, [[0, 0], [
-3, -3], [1, 1], [7, 7], [0, 0]]]], [[3, 4, 6, 1, 1], [0 < v, u = -(v^2+1)^(1/
2), x = 1, y < -1, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455
/524288], [1, 1], [-2, -2], [-1, -1]]]], [[3, 4, 6, 1, 2], [0 < v, u = -(v^2+1
)^(1/2), x = 1, y < -1, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [1, 1], [-2, -2], [0, 0]]]], [[3, 4, 6, 1, 3], [0 < v, u = -(v
^2+1)^(1/2), x = 1, y < -1, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576
, -741455/524288], [1, 1], [-2, -2], [1, 1]]]], [[3, 9, 5, 3, 1], [0 < v, And(
v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-
u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-3/8388608, -3/
8388608], [-2, -2]]]], [[3, 9, 5, 3, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)),
And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [
479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [-772605/1048576, -\
1545209/2097152]]]], [[3, 9, 5, 3, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 
And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2
+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-3/8388608, -3/
8388608], [-1/4194304, -1/4194304]]]], [[3, 9, 5, 3, 4], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1)
, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [193151/
262144, 772605/1048576]]]], [[3, 9, 5, 3, 5], [0 < v, And(v < u,u < (v^2+1)^(1
/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^
2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576],
[479311/2097152, 479311/2097152], [-3/8388608, -3/8388608], [2, 2]]]], [[1, 10
, 1, 2, 1], [v < 0, u = (v^2+1)^(1/2), x < -1, y = x, z < 0], [regular_chain,
[[-1, -1], [741455/524288, 1482911/1048576], [-2, -2], [-2, -2], [-1, -1]]]],
[[1, 10, 1, 2, 2], [v < 0, u = (v^2+1)^(1/2), x < -1, y = x, z = 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-2, -2], [-2, -2]
, [0, 0]]]], [[1, 10, 1, 2, 3], [v < 0, u = (v^2+1)^(1/2), x < -1, y = x, 0 <
z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-2, -2], [-2
, -2], [1, 1]]]], [[2, 1, 6, 1, 1], [v = 0, u < -2^(1/2), x = u^2-1, y < 0, z
= z], [regular_chain, [[0, 0], [-3, -3], [8, 8], [-1, -1], [0, 0]]]], [[3, 4,
6, 2, 1], [0 < v, u = -(v^2+1)^(1/2), x = 1, y = -1, z < 0], [regular_chain, [
[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1], [-1, -1]]]], [[3
, 4, 6, 2, 2], [0 < v, u = -(v^2+1)^(1/2), x = 1, y = -1, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1],
[0, 0]]]], [[3, 4, 6, 2, 3], [0 < v, u = -(v^2+1)^(1/2), x = 1, y = -1, 0 < z]
, [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1
], [1, 1]]]], [[3, 9, 6, 3, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, 
And(u^2-v^2-2 < y,y < -u^2+v^2+2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [0, 0], [-2, -2]]]], [[3,
9, 6, 3, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y,y
< -u^2+v^2+2), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [1, 1], [0, 0], [-772605/1048576, -1545209/2097152]
]]], [[3, 9, 6, 3, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, And(u^2-v^
2-2 < y,y < -u^2+v^2+2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))],
[regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [0, 0], [
-1/4194304, -1/4194304]]]], [[3, 9, 6, 3, 4], [0 < v, And(v < u,u < (v^2+1)^(1
/2)), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [0, 0], [
193151/262144, 772605/1048576]]]], [[3, 9, 6, 3, 5], [0 < v, And(v < u,u < (v^
2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), (-u^2+v^2+1)^(1/2) < z]
, [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [0, 0],
[2, 2]]]], [[1, 2, 2, 3, 1], [v < 0, u = -(v^2+2)^(1/2), x = -1, And(-2 < y,y
< 2), z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152],
[-1, -1], [0, 0], [0, 0]]]], [[1, 7, 3, 1, 1], [v < 0, And(v < u,u < -v), And(
u^2-v^2-1 < x,x < -1), y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2], [-2, -2], [-3, -3]]]], [[1, 7,
3, 1, 2], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), y < u^2-v^2-x-\
1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-3/2, -3/2],
[-2, -2], [-1482911/1048576, -741455/524288]]]], [[1, 7, 3, 1, 3], [v < 0, And
(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^
(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-3/2,
-3/2], [-2, -2], [0, 0]]]], [[1, 7, 3, 1, 4], [v < 0, And(v < u,u < -v), And(u
^2-v^2-1 < x,x < -1), y < u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain
, [[-1, -1], [0, 0], [-3/2, -3/2], [-2, -2], [741455/524288, 1482911/1048576]]
]], [[1, 7, 3, 1, 5], [v < 0, And(v < u,u < -v), And(u^2-v^2-1 < x,x < -1), y
< u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-3
/2, -3/2], [-2, -2], [3, 3]]]], [[2, 8, 2, 3, 1], [v = 0, u = 1, x = -1, And(-\
1 < y,y < 1), z < 0], [regular_chain, [[0, 0], [1, 1], [-1, -1], [0, 0], [-1,
-1]]]], [[2, 8, 2, 3, 2], [v = 0, u = 1, x = -1, And(-1 < y,y < 1), z = 0], [
regular_chain, [[0, 0], [1, 1], [-1, -1], [0, 0], [0, 0]]]], [[2, 8, 2, 3, 3],
[v = 0, u = 1, x = -1, And(-1 < y,y < 1), 0 < z], [regular_chain, [[0, 0], [1,
1], [-1, -1], [0, 0], [1, 1]]]], [[3, 1, 7, 4, 1], [0 < v, u < -(v^2+2)^(1/2),
u^2-v^2-1 < x, y = x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-3, -3], [8,
8], [1, 1], [0, 0]]]], [[3, 12, 2, 5, 1], [0 < v, u = (v^2+2)^(1/2), x = -1, 2
< y, z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [-1, -\
1], [3, 3], [0, 0]]]], [[1, 10, 1, 1, 1], [v < 0, u = (v^2+1)^(1/2), x < -1, y
< x, z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-2,
-2], [-3, -3], [-1, -1]]]], [[1, 10, 1, 1, 2], [v < 0, u = (v^2+1)^(1/2), x <
-1, y < x, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576]
, [-2, -2], [-3, -3], [0, 0]]]], [[1, 10, 1, 1, 3], [v < 0, u = (v^2+1)^(1/2),
x < -1, y < x, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [-2, -2], [-3, -3], [1, 1]]]], [[2, 1, 5, 5, 1], [v = 0, u < -2^(1/2
), And(1 < x,x < u^2-1), u^2-x-1 < y, z = z], [regular_chain, [[0, 0], [-3, -3
], [9/2, 9/2], [5, 5], [0, 0]]]], [[3, 4, 6, 3, 1], [0 < v, u = -(v^2+1)^(1/2)
, x = 1, And(-1 < y,y < 1), z < 0], [regular_chain, [[1, 1], [-1482911/1048576
, -741455/524288], [1, 1], [0, 0], [-1, -1]]]], [[3, 4, 6, 3, 2], [0 < v, u =
-(v^2+1)^(1/2), x = 1, And(-1 < y,y < 1), z = 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [1, 1], [0, 0], [0, 0]]]], [[3, 4, 6, 3, 3],
[0 < v, u = -(v^2+1)^(1/2), x = 1, And(-1 < y,y < 1), 0 < z], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [0, 0], [1, 1]]]], [[3, 9
, 6, 4, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, z < -
(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [1, 1], [1617841/1048576, 808921/524288], [-2, -2]]]], [[3, 9, 6, 4,
2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, z = -(-u^2+v^
2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1,
1], [1617841/1048576, 808921/524288], [-772605/1048576, -1545209/2097152]]]],
[[3, 9, 6, 4, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [1, 1], [1617841/1048576, 808921/524288],
[-1/4194304, -1/4194304]]]], [[3, 9, 6, 4, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), x = 1, y = -u^2+v^2+2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [1265743/1048576, 1265743/1048576], [1, 1], [1617841/1048576, 808921/524288]
, [193151/262144, 772605/1048576]]]], [[3, 9, 6, 4, 5], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, (-u^2+v^2+1)^(1/2) < z], [regular_chain
, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [1617841/1048576, 
808921/524288], [2, 2]]]], [[1, 2, 2, 2, 1], [v < 0, u = -(v^2+2)^(1/2), x = -\
1, y = -2, z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/
2097152], [-1, -1], [-2, -2], [0, 0]]]], [[1, 7, 2, 3, 1], [v < 0, And(v < u,u
< -v), x = u^2-v^2-1, 0 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -\
1], [0, 0], [-2, -2], [1, 1], [-3, -3]]]], [[1, 7, 2, 3, 2], [v < 0, And(v < u
,u < -v), x = u^2-v^2-1, 0 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1
, -1], [0, 0], [-2, -2], [1, 1], [-1482911/1048576, -741455/524288]]]], [[1, 7
, 2, 3, 3], [v < 0, And(v < u,u < -v), x = u^2-v^2-1, 0 < y, And(-(-u^2+v^2+1)
^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-2, -\
2], [1, 1], [0, 0]]]], [[1, 7, 2, 3, 4], [v < 0, And(v < u,u < -v), x = u^2-v^
2-1, 0 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-2, -\
2], [1, 1], [741455/524288, 1482911/1048576]]]], [[1, 7, 2, 3, 5], [v < 0, And
(v < u,u < -v), x = u^2-v^2-1, 0 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[-1, -1], [0, 0], [-2, -2], [1, 1], [3, 3]]]], [[2, 8, 2, 4, 1], [v = 0, u =
1, x = -1, y = 1, z < 0], [regular_chain, [[0, 0], [1, 1], [-1, -1], [1, 1], [
-1, -1]]]], [[2, 8, 2, 4, 2], [v = 0, u = 1, x = -1, y = 1, z = 0], [
regular_chain, [[0, 0], [1, 1], [-1, -1], [1, 1], [0, 0]]]], [[2, 8, 2, 4, 3],
[v = 0, u = 1, x = -1, y = 1, 0 < z], [regular_chain, [[0, 0], [1, 1], [-1, -1
], [1, 1], [1, 1]]]], [[3, 1, 7, 5, 1], [0 < v, u < -(v^2+2)^(1/2), u^2-v^2-1
< x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[1, 1], [-3, -3], [8, 8], [2, 2
], [0, 0]]]], [[3, 12, 2, 4, 1], [0 < v, u = (v^2+2)^(1/2), x = -1, y = 2, z =
z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [-1, -1], [2, 2
], [0, 0]]]], [[1, 10, 1, 4, 1], [v < 0, u = (v^2+1)^(1/2), x < -1, y = -x, z
< 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-2, -2], [
2, 2], [-1, -1]]]], [[1, 10, 1, 4, 2], [v < 0, u = (v^2+1)^(1/2), x < -1, y =
-x, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-2,
-2], [2, 2], [0, 0]]]], [[1, 10, 1, 4, 3], [v < 0, u = (v^2+1)^(1/2), x < -1,
y = -x, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [
-2, -2], [2, 2], [1, 1]]]], [[2, 1, 5, 4, 1], [v = 0, u < -2^(1/2), And(1 < x,
x < u^2-1), y = u^2-x-1, z = z], [regular_chain, [[0, 0], [-3, -3], [9/2, 9/2]
, [7/2, 7/2], [0, 0]]]], [[3, 4, 6, 4, 1], [0 < v, u = -(v^2+1)^(1/2), x = 1,
y = 1, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1
, 1], [1, 1], [-1, -1]]]], [[3, 4, 6, 4, 2], [0 < v, u = -(v^2+1)^(1/2), x = 1
, y = 1, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288],
[1, 1], [1, 1], [0, 0]]]], [[3, 4, 6, 4, 3], [0 < v, u = -(v^2+1)^(1/2), x = 1
, y = 1, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288],
[1, 1], [1, 1], [1, 1]]]], [[3, 9, 6, 1, 1], [0 < v, And(v < u,u < (v^2+1)^(1/
2)), x = 1, y < u^2-v^2-2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [1, 1], [-3, -3], [-2, -2]]]], [[3, 9, 6,
1, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, z = -(-u^2+
v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1
, 1], [-3, -3], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 6, 1, 3], [0 <
v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [1, 1], [-3, -3], [-1/4194304, -1/4194304]]]], [[3, 9, 6, 1,
4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, z = (-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1]
, [-3, -3], [193151/262144, 772605/1048576]]]], [[3, 9, 6, 1, 5], [0 < v, And(
v < u,u < (v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [-3, -3],
[2, 2]]]], [[1, 2, 2, 5, 1], [v < 0, u = -(v^2+2)^(1/2), x = -1, 2 < y, z = z]
, [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [-1, -1], [
3, 3], [0, 0]]]], [[1, 7, 2, 2, 1], [v < 0, And(v < u,u < -v), x = u^2-v^2-1,
y = 0, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-2, -2],
[0, 0], [-3, -3]]]], [[1, 7, 2, 2, 2], [v < 0, And(v < u,u < -v), x = u^2-v^2-\
1, y = 0, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-2, -2
], [0, 0], [-1482911/1048576, -741455/524288]]]], [[1, 7, 2, 2, 3], [v < 0, 
And(v < u,u < -v), x = u^2-v^2-1, y = 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2
+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-2, -2], [0, 0], [0, 0]]]
], [[1, 7, 2, 2, 4], [v < 0, And(v < u,u < -v), x = u^2-v^2-1, y = 0, z = (-u^
2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-2, -2], [0, 0], [741455/
524288, 1482911/1048576]]]], [[1, 7, 2, 2, 5], [v < 0, And(v < u,u < -v), x =
u^2-v^2-1, y = 0, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0],
[-2, -2], [0, 0], [3, 3]]]], [[2, 8, 2, 5, 1], [v = 0, u = 1, x = -1, 1 < y, z
< 0], [regular_chain, [[0, 0], [1, 1], [-1, -1], [2, 2], [-1, -1]]]], [[2, 8,
2, 5, 2], [v = 0, u = 1, x = -1, 1 < y, z = 0], [regular_chain, [[0, 0], [1, 1
], [-1, -1], [2, 2], [0, 0]]]], [[2, 8, 2, 5, 3], [v = 0, u = 1, x = -1, 1 < y
, 0 < z], [regular_chain, [[0, 0], [1, 1], [-1, -1], [2, 2], [1, 1]]]], [[3, 1
, 7, 2, 1], [0 < v, u < -(v^2+2)^(1/2), u^2-v^2-1 < x, y = u^2-v^2-x-1, z = z]
, [regular_chain, [[1, 1], [-3, -3], [8, 8], [-1, -1], [0, 0]]]], [[3, 12, 3,
2, 1], [0 < v, u = (v^2+2)^(1/2), And(-1 < x,x < 1), y = x-1, z = z], [
regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [0, 0], [-1, -1], [0
, 0]]]], [[1, 10, 1, 3, 1], [v < 0, u = (v^2+1)^(1/2), x < -1, And(x < y,y < -
x), z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-2,
-2], [0, 0], [-1, -1]]]], [[1, 10, 1, 3, 2], [v < 0, u = (v^2+1)^(1/2), x < -1
, And(x < y,y < -x), z = 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [-2, -2], [0, 0], [0, 0]]]], [[1, 10, 1, 3, 3], [v < 0, u =
(v^2+1)^(1/2), x < -1, And(x < y,y < -x), 0 < z], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [-2, -2], [0, 0], [1, 1]]]], [[2, 1, 5, 3, 1]
, [v = 0, u < -2^(1/2), And(1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), z
= z], [regular_chain, [[0, 0], [-3, -3], [9/2, 9/2], [0, 0], [0, 0]]]], [[3, 4
, 6, 5, 1], [0 < v, u = -(v^2+1)^(1/2), x = 1, 1 < y, z < 0], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [2, 2], [-1, -1]]]], [[3,
4, 6, 5, 2], [0 < v, u = -(v^2+1)^(1/2), x = 1, 1 < y, z = 0], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [2, 2], [0, 0]]]], [[3, 4
, 6, 5, 3], [0 < v, u = -(v^2+1)^(1/2), x = 1, 1 < y, 0 < z], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [1, 1], [2, 2], [1, 1]]]], [[3, 9
, 6, 2, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, z < -(
-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576
], [1, 1], [-3235683/2097152, -1617841/1048576], [-2, -2]]]], [[3, 9, 6, 2, 2]
, [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, z = -(-u^2+v^2+1
)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1],
[-3235683/2097152, -1617841/1048576], [-772605/1048576, -1545209/2097152]]]],
[[3, 9, 6, 2, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [1, 1], [-3235683/2097152, -1617841/
1048576], [-1/4194304, -1/4194304]]]], [[3, 9, 6, 2, 4], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [-3235683/2097152, -\
1617841/1048576], [193151/262144, 772605/1048576]]]], [[3, 9, 6, 2, 5], [0 < v
, And(v < u,u < (v^2+1)^(1/2)), x = 1, y = u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z],
[regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [1, 1], [-3235683
/2097152, -1617841/1048576], [2, 2]]]], [[1, 2, 2, 4, 1], [v < 0, u = -(v^2+2)
^(1/2), x = -1, y = 2, z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -\
3632373/2097152], [-1, -1], [2, 2], [0, 0]]]], [[1, 7, 2, 1, 1], [v < 0, And(v
< u,u < -v), x = u^2-v^2-1, y < 0, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [0, 0], [-2, -2], [-1, -1], [-3, -3]]]], [[1, 7, 2, 1, 2], [v < 0, 
And(v < u,u < -v), x = u^2-v^2-1, y < 0, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-2, -2], [-1, -1], [-1482911/1048576, -\
741455/524288]]]], [[1, 7, 2, 1, 3], [v < 0, And(v < u,u < -v), x = u^2-v^2-1,
y < 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [
[-1, -1], [0, 0], [-2, -2], [-1, -1], [0, 0]]]], [[1, 7, 2, 1, 4], [v < 0, And
(v < u,u < -v), x = u^2-v^2-1, y < 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain,
[[-1, -1], [0, 0], [-2, -2], [-1, -1], [741455/524288, 1482911/1048576]]]], [[
1, 7, 2, 1, 5], [v < 0, And(v < u,u < -v), x = u^2-v^2-1, y < 0, (-u^2+v^2+1)^
(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-2, -2], [-1, -1], [3, 3]]]],
[[2, 8, 3, 1, 1], [v = 0, u = 1, And(-1 < x,x < 0), y < x, z < 0], [
regular_chain, [[0, 0], [1, 1], [-1/2, -1/2], [-2, -2], [-1, -1]]]], [[2, 8, 3
, 1, 2], [v = 0, u = 1, And(-1 < x,x < 0), y < x, z = 0], [regular_chain, [[0,
0], [1, 1], [-1/2, -1/2], [-2, -2], [0, 0]]]], [[2, 8, 3, 1, 3], [v = 0, u = 1
, And(-1 < x,x < 0), y < x, 0 < z], [regular_chain, [[0, 0], [1, 1], [-1/2, -1
/2], [-2, -2], [1, 1]]]], [[3, 1, 7, 3, 1], [0 < v, u < -(v^2+2)^(1/2), u^2-v^
2-1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [regular_chain, [[1, 1]
, [-3, -3], [8, 8], [0, 0], [0, 0]]]], [[3, 12, 3, 1, 1], [0 < v, u = (v^2+2)^
(1/2), And(-1 < x,x < 1), y < x-1, z = z], [regular_chain, [[1, 1], [908093/
524288, 1816187/1048576], [0, 0], [-2, -2], [0, 0]]]], [[1, 2, 5, 3, 1], [v <
0, u = -(v^2+2)^(1/2), 1 < x, And(1-x < y,y < x-1), z = z], [regular_chain, [[
-1, -1], [-1816187/1048576, -3632373/2097152], [2, 2], [0, 0], [0, 0]]]], [[1,
6, 3, 1, 1], [v < 0, u = v, And(-1 < x,x < 1), y < -1-x, z < -1], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [-2, -2], [-2, -2]]]], [[1, 6, 3,
1, 2], [v < 0, u = v, And(-1 < x,x < 1), y < -1-x, z = -1], [regular_chain, [[
-1, -1], [-1, -1], [0, 0], [-2, -2], [-1, -1]]]], [[1, 6, 3, 1, 3], [v < 0, u
= v, And(-1 < x,x < 1), y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[-1, -1
], [-1, -1], [0, 0], [-2, -2], [0, 0]]]], [[1, 6, 3, 1, 4], [v < 0, u = v, And
(-1 < x,x < 1), y < -1-x, z = 1], [regular_chain, [[-1, -1], [-1, -1], [0, 0],
[-2, -2], [1, 1]]]], [[1, 6, 3, 1, 5], [v < 0, u = v, And(-1 < x,x < 1), y < -\
1-x, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [-2, -2], [2, 2]]]],
[[2, 9, 2, 1, 1], [v = 0, And(1 < u,u < 2^(1/2)), x = -1, y < -u^2, z = z], [
regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [-1, -1], [-3, -3]
, [0, 0]]]], [[3, 1, 6, 2, 1], [0 < v, u < -(v^2+2)^(1/2), x = u^2-v^2-1, y =
0, z = z], [regular_chain, [[1, 1], [-3, -3], [7, 7], [0, 0], [0, 0]]]], [[3,
12, 5, 5, 1], [0 < v, u = (v^2+2)^(1/2), 1 < x, x-1 < y, z = z], [
regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [2, 2], [2, 2], [0,
0]]]], [[1, 10, 2, 2, 1], [v < 0, u = (v^2+1)^(1/2), x = -1, y = -1, z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1, -1], [-1, -1]
, [-1, -1]]]], [[1, 10, 2, 2, 2], [v < 0, u = (v^2+1)^(1/2), x = -1, y = -1, z
= 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1, -1], [
-1, -1], [0, 0]]]], [[1, 10, 2, 2, 3], [v < 0, u = (v^2+1)^(1/2), x = -1, y =
-1, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1,
-1], [-1, -1], [1, 1]]]], [[1, 13, 6, 3, 1], [v < 0, (v^2+2)^(1/2) < u, x = u^
2-v^2-1, 0 < y, z = z], [regular_chain, [[-1, -1], [3, 3], [7, 7], [1, 1], [0,
0]]]], [[3, 5, 3, 5, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x
< u^2-v^2-1), u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304]
, [2, 2], [-2, -2]]]], [[3, 5, 3, 5, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v
), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [-772605/1048576, -1545209/2097152]]]], [[
3, 5, 3, 5, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2
-1), u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [-1/4194304, -1/4194304]]]], [[3, 5, 3, 5,
4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), u^2-v^2
-x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576,
-1265743/1048576], [-3235683/4194304, -3235683/4194304], [2, 2], [193151/
262144, 772605/1048576]]]], [[3, 5, 3, 5, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u
< -v), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [2, 2]]]], [[3, 9, 3, 3, 1], [0 < v, And(v
< u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2
-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576
, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [-2, -2]]]],
[[3, 9, 3, 3, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2
-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304,
-3235683/4194304], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 3,
3, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), And(x-
u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(
1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683
/4194304, -3235683/4194304], [0, 0], [-1/4194304, -1/4194304]]]], [[3, 9, 3, 3
, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), And(x-u
^2+v^2+1 < y,y < u^2-v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1
], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [
0, 0], [193151/262144, 772605/1048576]]]], [[3, 9, 3, 3, 5], [0 < v, And(v < u
,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^
2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [2, 2]]]], [[1
, 2, 5, 4, 1], [v < 0, u = -(v^2+2)^(1/2), 1 < x, y = x-1, z = z], [
regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [2, 2], [1, 1]
, [0, 0]]]], [[1, 6, 3, 2, 1], [v < 0, u = v, And(-1 < x,x < 1), y = -1-x, z <
-1], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [-1, -1], [-2, -2]]]], [[1,
6, 3, 2, 2], [v < 0, u = v, And(-1 < x,x < 1), y = -1-x, z = -1], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [-1, -1], [-1, -1]]]], [[1, 6, 3,
2, 3], [v < 0, u = v, And(-1 < x,x < 1), y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [-1, -1], [0, 0]]]], [[1, 6, 3, 2,
4], [v < 0, u = v, And(-1 < x,x < 1), y = -1-x, z = 1], [regular_chain, [[-1,
-1], [-1, -1], [0, 0], [-1, -1], [1, 1]]]], [[1, 6, 3, 2, 5], [v < 0, u = v, 
And(-1 < x,x < 1), y = -1-x, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [0,
0], [-1, -1], [2, 2]]]], [[2, 9, 1, 5, 1], [v = 0, And(1 < u,u < 2^(1/2)), x <
-1, u^2-x-1 < y, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/
1048576], [-2, -2], [4, 4], [0, 0]]]], [[3, 1, 6, 1, 1], [0 < v, u < -(v^2+2)^
(1/2), x = u^2-v^2-1, y < 0, z = z], [regular_chain, [[1, 1], [-3, -3], [7, 7]
, [-1, -1], [0, 0]]]], [[3, 13, 1, 1, 1], [0 < v, (v^2+2)^(1/2) < u, x < -1, y
< x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [3, 3], [-2, -2], [-10, -10],
[0, 0]]]], [[1, 10, 2, 3, 1], [v < 0, u = (v^2+1)^(1/2), x = -1, And(-1 < y,y
< 1), z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1
, -1], [0, 0], [-1, -1]]]], [[1, 10, 2, 3, 2], [v < 0, u = (v^2+1)^(1/2), x =
-1, And(-1 < y,y < 1), z = 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [-1, -1], [0, 0], [0, 0]]]], [[1, 10, 2, 3, 3], [v < 0, u =
(v^2+1)^(1/2), x = -1, And(-1 < y,y < 1), 0 < z], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [-1, -1], [0, 0], [1, 1]]]], [[1, 13, 7, 1, 1
], [v < 0, (v^2+2)^(1/2) < u, u^2-v^2-1 < x, y < u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [3, 3], [8, 8], [-2, -2], [0, 0]]]], [[3, 5, 3, 4, 1
], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y = u^2-
v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576,
-1265743/1048576], [-3235683/4194304, -3235683/4194304], [239655/1048576, 
29957/131072], [-2, -2]]]], [[3, 5, 3, 4, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u
< -v), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [239655/1048576, 29957/131072], [-772605/1048576,
-1545209/2097152]]]], [[3, 5, 3, 4, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v)
, And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [239655/1048576, 29957/131072]
, [-1/4194304, -1/4194304]]]], [[3, 5, 3, 4, 4], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)]
, [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [239655/1048576, 29957/131072], [193151/262144, 
772605/1048576]]]], [[3, 5, 3, 4, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [239655/1048576, 29957/131072], [2, 2]]]], [[3, 9,
3, 2, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y =
x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [-29957/
131072, -239655/1048576], [-2, -2]]]], [[3, 9, 3, 2, 2], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^
(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683
/4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [-772605/
1048576, -1545209/2097152]]]], [[3, 9, 3, 2, 3], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) <
z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743
/1048576], [-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/
1048576], [-1/4194304, -1/4194304]]]], [[3, 9, 3, 2, 4], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(
1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [193151/262144,
772605/1048576]]]], [[3, 9, 3, 2, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), 
And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304,
-3235683/4194304], [-29957/131072, -239655/1048576], [2, 2]]]], [[1, 2, 5, 1,
1], [v < 0, u = -(v^2+2)^(1/2), 1 < x, y < 1-x, z = z], [regular_chain, [[-1,
-1], [-1816187/1048576, -3632373/2097152], [2, 2], [-2, -2], [0, 0]]]], [[1, 6
, 3, 3, 1], [v < 0, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z < -1],
[regular_chain, [[-1, -1], [-1, -1], [0, 0], [0, 0], [-2, -2]]]], [[1, 6, 3, 3
, 2], [v < 0, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z = -1], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [0, 0], [-1, -1]]]], [[1, 6, 3, 3,
3], [v < 0, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), And(-1 < z,z < 1)
], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [0, 0], [0, 0]]]], [[1, 6, 3,
3, 4], [v < 0, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z = 1], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [0, 0], [1, 1]]]], [[1, 6, 3, 3, 5
], [v < 0, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), 1 < z], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [0, 0], [2, 2]]]], [[2, 9, 1, 4, 1
], [v = 0, And(1 < u,u < 2^(1/2)), x < -1, y = u^2-x-1, z = z], [regular_chain
, [[0, 0], [1265743/1048576, 1265743/1048576], [-2, -2], [1288231/524288, 
2576463/1048576], [0, 0]]]], [[3, 1, 7, 1, 1], [0 < v, u < -(v^2+2)^(1/2), u^2
-v^2-1 < x, y < u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [-3, -3], [8, 8]
, [-2, -2], [0, 0]]]], [[3, 12, 5, 3, 1], [0 < v, u = (v^2+2)^(1/2), 1 < x, 
And(1-x < y,y < x-1), z = z], [regular_chain, [[1, 1], [908093/524288, 1816187
/1048576], [2, 2], [0, 0], [0, 0]]]], [[1, 10, 1, 5, 1], [v < 0, u = (v^2+1)^(
1/2), x < -1, -x < y, z < 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [-2, -2], [3, 3], [-1, -1]]]], [[1, 10, 1, 5, 2], [v < 0, u
= (v^2+1)^(1/2), x < -1, -x < y, z = 0], [regular_chain, [[-1, -1], [741455/
524288, 1482911/1048576], [-2, -2], [3, 3], [0, 0]]]], [[1, 10, 1, 5, 3], [v <
0, u = (v^2+1)^(1/2), x < -1, -x < y, 0 < z], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [-2, -2], [3, 3], [1, 1]]]], [[1, 13, 7, 2, 1
], [v < 0, (v^2+2)^(1/2) < u, u^2-v^2-1 < x, y = u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [3, 3], [8, 8], [-1, -1], [0, 0]]]], [[3, 5, 3, 3, 1
], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), And(x-u^
2+v^2+1 < y,y < u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1
], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304],
[0, 0], [-2, -2]]]], [[3, 5, 3, 3, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^
2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [0, 0], [-772605/1048576, -1545209/2097152
]]]], [[3, 5, 3, 3, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x <
u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,
z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743
/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [-1/4194304, -1/
4194304]]]], [[3, 5, 3, 3, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1
< x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = (-u^2+v^2+1)^(1/
2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [0, 0], [193151/262144, 772605/1048576]]]], [[3, 5
, 3, 3, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1),
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/
4194304], [0, 0], [2, 2]]]], [[3, 9, 3, 5, 1], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304,
-3235683/4194304], [2, 2], [-2, -2]]]], [[3, 9, 3, 5, 2], [0 < v, And(v < u,u
< (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = -(-u^2+v^2+1
)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [2, 2], [-772605/1048576, -1545209/2097152
]]]], [[3, 9, 3, 5, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u
^2-v^2-1), u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2)
)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [-1/4194304, -1/4194304]]]], [[3, 9, 3, 5,
4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x
-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-3235683/4194304, -3235683/4194304], [2, 2], [193151/262144
, 772605/1048576]]]], [[3, 9, 3, 5, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)),
And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304,
-3235683/4194304], [2, 2], [2, 2]]]], [[1, 2, 5, 2, 1], [v < 0, u = -(v^2+2)^(
1/2), 1 < x, y = 1-x, z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -\
3632373/2097152], [2, 2], [-1, -1], [0, 0]]]], [[1, 6, 3, 4, 1], [v < 0, u = v
, And(-1 < x,x < 1), y = x+1, z < -1], [regular_chain, [[-1, -1], [-1, -1], [0
, 0], [1, 1], [-2, -2]]]], [[1, 6, 3, 4, 2], [v < 0, u = v, And(-1 < x,x < 1),
y = x+1, z = -1], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [1, 1], [-1, -1
]]]], [[1, 6, 3, 4, 3], [v < 0, u = v, And(-1 < x,x < 1), y = x+1, And(-1 < z,
z < 1)], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [1, 1], [0, 0]]]], [[1,
6, 3, 4, 4], [v < 0, u = v, And(-1 < x,x < 1), y = x+1, z = 1], [regular_chain
, [[-1, -1], [-1, -1], [0, 0], [1, 1], [1, 1]]]], [[1, 6, 3, 4, 5], [v < 0, u
= v, And(-1 < x,x < 1), y = x+1, 1 < z], [regular_chain, [[-1, -1], [-1, -1],
[0, 0], [1, 1], [2, 2]]]], [[2, 9, 1, 3, 1], [v = 0, And(1 < u,u < 2^(1/2)), x
< -1, And(x-u^2+1 < y,y < u^2-x-1), z = z], [regular_chain, [[0, 0], [1265743/
1048576, 1265743/1048576], [-2, -2], [0, 0], [0, 0]]]], [[3, 1, 6, 3, 1], [0 <
v, u < -(v^2+2)^(1/2), x = u^2-v^2-1, 0 < y, z = z], [regular_chain, [[1, 1],
[-3, -3], [7, 7], [1, 1], [0, 0]]]], [[3, 12, 5, 4, 1], [0 < v, u = (v^2+2)^(1
/2), 1 < x, y = x-1, z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/
1048576], [2, 2], [1, 1], [0, 0]]]], [[1, 10, 2, 1, 1], [v < 0, u = (v^2+1)^(1
/2), x = -1, y < -1, z < 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [-1, -1], [-2, -2], [-1, -1]]]], [[1, 10, 2, 1, 2], [v < 0,
u = (v^2+1)^(1/2), x = -1, y < -1, z = 0], [regular_chain, [[-1, -1], [741455/
524288, 1482911/1048576], [-1, -1], [-2, -2], [0, 0]]]], [[1, 10, 2, 1, 3], [v
< 0, u = (v^2+1)^(1/2), x = -1, y < -1, 0 < z], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [-1, -1], [-2, -2], [1, 1]]]], [[1, 13, 7, 3,
1], [v < 0, (v^2+2)^(1/2) < u, u^2-v^2-1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^
2+1), z = z], [regular_chain, [[-1, -1], [3, 3], [8, 8], [0, 0], [0, 0]]]], [[
3, 5, 3, 2, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2
-1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304], [-\
29957/131072, -239655/1048576], [-2, -2]]]], [[3, 5, 3, 2, 2], [0 < v, And(-(v
^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = -(-u^
2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576]
, [-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [-\
772605/1048576, -1545209/2097152]]]], [[3, 5, 3, 2, 3], [0 < v, And(-(v^2+1)^(
1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1
)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-3235683/4194304, -3235683/4194304], [-29957/
131072, -239655/1048576], [-1/4194304, -1/4194304]]]], [[3, 5, 3, 2, 4], [0 <
v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/
1048576], [193151/262144, 772605/1048576]]]], [[3, 5, 3, 2, 5], [0 < v, And(-(
v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, (-u^2+v^
2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576]
, [-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [2,
2]]]], [[3, 9, 3, 4, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x <
u^2-v^2-1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [
239655/1048576, 29957/131072], [-2, -2]]]], [[3, 9, 3, 4, 2], [0 < v, And(v <
u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = -(-u^2+v
^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [239655/1048576, 29957/131072], [-772605/
1048576, -1545209/2097152]]]], [[3, 9, 3, 4, 3], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) <
z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743
/1048576], [-3235683/4194304, -3235683/4194304], [239655/1048576, 29957/131072
], [-1/4194304, -1/4194304]]]], [[3, 9, 3, 4, 4], [0 < v, And(v < u,u < (v^2+1
)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)],
[regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304
, -3235683/4194304], [239655/1048576, 29957/131072], [193151/262144, 772605/
1048576]]]], [[3, 9, 3, 4, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 <
x,x < u^2-v^2-1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[
1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304
], [239655/1048576, 29957/131072], [2, 2]]]], [[1, 10, 3, 1, 1], [v < 0, u = (
v^2+1)^(1/2), And(-1 < x,x < 0), y < x, z < 0], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [-1/2, -1/2], [-2, -2], [-1, -1]]]], [[1, 10,
3, 1, 2], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y < x, z = 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [-2,
-2], [0, 0]]]], [[1, 10, 3, 1, 3], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0
), y < x, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576],
[-1/2, -1/2], [-2, -2], [1, 1]]]], [[1, 13, 7, 4, 1], [v < 0, (v^2+2)^(1/2) <
u, u^2-v^2-1 < x, y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [3, 3],
[8, 8], [1, 1], [0, 0]]]], [[3, 5, 5, 1, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u
< -v), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152,
479311/2097152], [-2, -2], [-2, -2]]]], [[3, 5, 5, 1, 2], [0 < v, And(-(v^2+1)
^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [
479311/2097152, 479311/2097152], [-2, -2], [-772605/1048576, -1545209/2097152]
]]], [[3, 5, 5, 1, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 <
x,x < 1), y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))
], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/
2097152, 479311/2097152], [-2, -2], [-1/4194304, -1/4194304]]]], [[3, 5, 5, 1,
4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(u^2-v^2-1 < x,x < 1), y < u^2-
v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576,
-1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2], [193151/262144,
772605/1048576]]]], [[3, 5, 5, 1, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [479311/2097152,
479311/2097152], [-2, -2], [2, 2]]]], [[3, 9, 4, 2, 1], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, z < -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/
1048576], [0, 0], [-2, -2]]]], [[3, 9, 4, 2, 2], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), x = u^2-v^2-1, y = 0, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [
0, 0], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 4, 2, 3], [0 < v, And(v
< u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [-1138531/2097152, -569265/1048576], [0, 0], [-1/4194304, -1/4194304
]]]], [[3, 9, 4, 2, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y
= 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-1138531/2097152, -569265/1048576], [0, 0], [193151/262144,
772605/1048576]]]], [[3, 9, 4, 2, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x
= u^2-v^2-1, y = 0, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743
/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [0, 0], [2, 2
]]]], [[1, 2, 4, 2, 1], [v < 0, u = -(v^2+2)^(1/2), x = 1, y = 0, z = z], [
regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [1, 1], [0, 0]
, [0, 0]]]], [[1, 6, 1, 5, 1], [v < 0, u = v, x < -1, -1-x < y, z < -1], [
regular_chain, [[-1, -1], [-1, -1], [-2, -2], [2, 2], [-2, -2]]]], [[1, 6, 1,
5, 2], [v < 0, u = v, x < -1, -1-x < y, z = -1], [regular_chain, [[-1, -1], [-\
1, -1], [-2, -2], [2, 2], [-1, -1]]]], [[1, 6, 1, 5, 3], [v < 0, u = v, x < -1
, -1-x < y, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [-2, -2],
[2, 2], [0, 0]]]], [[1, 6, 1, 5, 4], [v < 0, u = v, x < -1, -1-x < y, z = 1],
[regular_chain, [[-1, -1], [-1, -1], [-2, -2], [2, 2], [1, 1]]]], [[1, 6, 1, 5
, 5], [v < 0, u = v, x < -1, -1-x < y, 1 < z], [regular_chain, [[-1, -1], [-1,
-1], [-2, -2], [2, 2], [2, 2]]]], [[2, 9, 1, 2, 1], [v = 0, And(1 < u,u < 2^(1
/2)), x < -1, y = x-u^2+1, z = z], [regular_chain, [[0, 0], [1265743/1048576,
1265743/1048576], [-2, -2], [-2576463/1048576, -1288231/524288], [0, 0]]]], [[
3, 1, 5, 3, 1], [0 < v, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), And(x-u^
2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[1, 1], [-3, -3], [4, 4
], [0, 0], [0, 0]]]], [[3, 12, 5, 1, 1], [0 < v, u = (v^2+2)^(1/2), 1 < x, y <
1-x, z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [2, 2]
, [-2, -2], [0, 0]]]], [[1, 10, 3, 2, 1], [v < 0, u = (v^2+1)^(1/2), And(-1 <
x,x < 0), y = x, z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [-1/2, -1/2], [-1/2, -1/2], [-1, -1]]]], [[1, 10, 3, 2, 2], [v < 0,
u = (v^2+1)^(1/2), And(-1 < x,x < 0), y = x, z = 0], [regular_chain, [[-1, -1]
, [741455/524288, 1482911/1048576], [-1/2, -1/2], [-1/2, -1/2], [0, 0]]]], [[1
, 10, 3, 2, 3], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y = x, 0 < z], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [-1/
2, -1/2], [1, 1]]]], [[1, 13, 7, 5, 1], [v < 0, (v^2+2)^(1/2) < u, u^2-v^2-1 <
x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[-1, -1], [3, 3], [8, 8], [2, 2],
[0, 0]]]], [[3, 5, 4, 3, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v
^2-1, 0 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [-2,
-2]]]], [[3, 5, 4, 3, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-\
1, 0 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576
, -1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [-772605/
1048576, -1545209/2097152]]]], [[3, 5, 4, 3, 3], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), x = u^2-v^2-1, 0 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^
(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-\
1138531/2097152, -569265/1048576], [1, 1], [-1/4194304, -1/4194304]]]], [[3, 5
, 4, 3, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-1, 0 < y, z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-1138531/2097152, -569265/1048576], [1, 1], [193151/262144, 772605/
1048576]]]], [[3, 5, 4, 3, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2
-v^2-1, 0 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [2, 2
]]]], [[3, 9, 4, 1, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y
< 0, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-1138531/2097152, -569265/1048576], [-1, -1], [-2, -2]]]],
[[3, 9, 4, 1, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y < 0,
z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [-1138531/2097152, -569265/1048576], [-1, -1], [-772605/1048576, -\
1545209/2097152]]]], [[3, 9, 4, 1, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x
= u^2-v^2-1, y < 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1138531/2097152,
-569265/1048576], [-1, -1], [-1/4194304, -1/4194304]]]], [[3, 9, 4, 1, 4], [0
< v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y < 0, z = (-u^2+v^2+1)^(1/2
)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1138531/
2097152, -569265/1048576], [-1, -1], [193151/262144, 772605/1048576]]]], [[3,
9, 4, 1, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y < 0, (-u^2
+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576
], [-1138531/2097152, -569265/1048576], [-1, -1], [2, 2]]]], [[1, 2, 4, 3, 1],
[v < 0, u = -(v^2+2)^(1/2), x = 1, 0 < y, z = z], [regular_chain, [[-1, -1], [
-1816187/1048576, -3632373/2097152], [1, 1], [1, 1], [0, 0]]]], [[1, 6, 2, 1,
1], [v < 0, u = v, x = -1, y < 0, z < -1], [regular_chain, [[-1, -1], [-1, -1]
, [-1, -1], [-1, -1], [-2, -2]]]], [[1, 6, 2, 1, 2], [v < 0, u = v, x = -1, y
< 0, z = -1], [regular_chain, [[-1, -1], [-1, -1], [-1, -1], [-1, -1], [-1, -1
]]]], [[1, 6, 2, 1, 3], [v < 0, u = v, x = -1, y < 0, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [-1, -1], [-1, -1], [0, 0]]]], [[1, 6, 2,
1, 4], [v < 0, u = v, x = -1, y < 0, z = 1], [regular_chain, [[-1, -1], [-1, -\
1], [-1, -1], [-1, -1], [1, 1]]]], [[1, 6, 2, 1, 5], [v < 0, u = v, x = -1, y
< 0, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [-1, -1], [-1, -1], [2, 2]]]
], [[2, 9, 1, 1, 1], [v = 0, And(1 < u,u < 2^(1/2)), x < -1, y < x-u^2+1, z =
z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [-2, -2], [-4
, -4], [0, 0]]]], [[3, 1, 5, 2, 1], [0 < v, u < -(v^2+2)^(1/2), And(1 < x,x <
u^2-v^2-1), y = x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-3, -3], [4, 4]
, [-3, -3], [0, 0]]]], [[3, 12, 5, 2, 1], [0 < v, u = (v^2+2)^(1/2), 1 < x, y
= 1-x, z = z], [regular_chain, [[1, 1], [908093/524288, 1816187/1048576], [2,
2], [-1, -1], [0, 0]]]], [[1, 10, 2, 4, 1], [v < 0, u = (v^2+1)^(1/2), x = -1,
y = 1, z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-\
1, -1], [1, 1], [-1, -1]]]], [[1, 10, 2, 4, 2], [v < 0, u = (v^2+1)^(1/2), x =
-1, y = 1, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576]
, [-1, -1], [1, 1], [0, 0]]]], [[1, 10, 2, 4, 3], [v < 0, u = (v^2+1)^(1/2), x
= -1, y = 1, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [-1, -1], [1, 1], [1, 1]]]], [[2, 1, 1, 1, 1], [v = 0, u < -2^(1/2),
x < -1, y < x-u^2+1, z = z], [regular_chain, [[0, 0], [-3, -3], [-2, -2], [-11
, -11], [0, 0]]]], [[3, 5, 4, 2, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x
= u^2-v^2-1, y = 0, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [-1138531/2097152, -569265/1048576], [0, 0
], [-2, -2]]]], [[3, 5, 4, 2, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x =
u^2-v^2-1, y = 0, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743
/1048576, -1265743/1048576], [-1138531/2097152, -569265/1048576], [0, 0], [-\
772605/1048576, -1545209/2097152]]]], [[3, 5, 4, 2, 3], [0 < v, And(-(v^2+1)^(
1/2) < u,u < -v), x = u^2-v^2-1, y = 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+
v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576],
[-1138531/2097152, -569265/1048576], [0, 0], [-1/4194304, -1/4194304]]]], [[3,
5, 4, 2, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-1, y = 0, z =
(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-1138531/2097152, -569265/1048576], [0, 0], [193151/262144, 772605/
1048576]]]], [[3, 5, 4, 2, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2
-v^2-1, y = 0, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-1138531/2097152, -569265/1048576], [0, 0], [2, 2
]]]], [[3, 9, 5, 1, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 <
x,x < 1), y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2]
, [-2, -2]]]], [[3, 9, 5, 1, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2
-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152],
[-2, -2], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 5, 1, 3], [0 < v, 
And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, And(-
(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2],
[-1/4194304, -1/4194304]]]], [[3, 9, 5, 1, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [479311/2097152, 
479311/2097152], [-2, -2], [193151/262144, 772605/1048576]]]], [[3, 9, 5, 1, 5
], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2
-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2], [2, 2]]]], [[1,
2, 3, 5, 1], [v < 0, u = -(v^2+2)^(1/2), And(-1 < x,x < 1), 1-x < y, z = z], [
regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [0, 0], [2, 2]
, [0, 0]]]], [[1, 6, 2, 2, 1], [v < 0, u = v, x = -1, y = 0, z < -1], [
regular_chain, [[-1, -1], [-1, -1], [-1, -1], [0, 0], [-2, -2]]]], [[1, 6, 2,
2, 2], [v < 0, u = v, x = -1, y = 0, z = -1], [regular_chain, [[-1, -1], [-1,
-1], [-1, -1], [0, 0], [-1, -1]]]], [[1, 6, 2, 2, 3], [v < 0, u = v, x = -1, y
= 0, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [-1, -1], [0, 0]
, [0, 0]]]], [[1, 6, 2, 2, 4], [v < 0, u = v, x = -1, y = 0, z = 1], [
regular_chain, [[-1, -1], [-1, -1], [-1, -1], [0, 0], [1, 1]]]], [[1, 6, 2, 2,
5], [v < 0, u = v, x = -1, y = 0, 1 < z], [regular_chain, [[-1, -1], [-1, -1],
[-1, -1], [0, 0], [2, 2]]]], [[2, 8, 7, 5, 1], [v = 0, u = 1, 1 < x, x < y, z
< 0], [regular_chain, [[0, 0], [1, 1], [2, 2], [3, 3], [-1, -1]]]], [[2, 8, 7,
5, 2], [v = 0, u = 1, 1 < x, x < y, z = 0], [regular_chain, [[0, 0], [1, 1], [
2, 2], [3, 3], [0, 0]]]], [[2, 8, 7, 5, 3], [v = 0, u = 1, 1 < x, x < y, 0 < z
], [regular_chain, [[0, 0], [1, 1], [2, 2], [3, 3], [1, 1]]]], [[3, 1, 5, 5, 1
], [0 < v, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z =
z], [regular_chain, [[1, 1], [-3, -3], [4, 4], [4, 4], [0, 0]]]], [[3, 12, 4,
2, 1], [0 < v, u = (v^2+2)^(1/2), x = 1, y = 0, z = z], [regular_chain, [[1, 1
], [908093/524288, 1816187/1048576], [1, 1], [0, 0], [0, 0]]]], [[1, 10, 2, 5,
1], [v < 0, u = (v^2+1)^(1/2), x = -1, 1 < y, z < 0], [regular_chain, [[-1, -1
], [741455/524288, 1482911/1048576], [-1, -1], [2, 2], [-1, -1]]]], [[1, 10, 2
, 5, 2], [v < 0, u = (v^2+1)^(1/2), x = -1, 1 < y, z = 0], [regular_chain, [[-\
1, -1], [741455/524288, 1482911/1048576], [-1, -1], [2, 2], [0, 0]]]], [[1, 10
, 2, 5, 3], [v < 0, u = (v^2+1)^(1/2), x = -1, 1 < y, 0 < z], [regular_chain,
[[-1, -1], [741455/524288, 1482911/1048576], [-1, -1], [2, 2], [1, 1]]]], [[2,
1, 1, 2, 1], [v = 0, u < -2^(1/2), x < -1, y = x-u^2+1, z = z], [regular_chain
, [[0, 0], [-3, -3], [-2, -2], [-10, -10], [0, 0]]]], [[3, 5, 4, 1, 1], [0 < v
, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-1, y < 0, z < -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1138531/
2097152, -569265/1048576], [-1, -1], [-2, -2]]]], [[3, 5, 4, 1, 2], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-1, y < 0, z = -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1138531/
2097152, -569265/1048576], [-1, -1], [-772605/1048576, -1545209/2097152]]]], [
[3, 5, 4, 1, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-1, y < 0,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1],
[-1265743/1048576, -1265743/1048576], [-1138531/2097152, -569265/1048576], [-1
, -1], [-1/4194304, -1/4194304]]]], [[3, 5, 4, 1, 4], [0 < v, And(-(v^2+1)^(1/
2) < u,u < -v), x = u^2-v^2-1, y < 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [-1265743/1048576, -1265743/1048576], [-1138531/2097152, -569265/
1048576], [-1, -1], [193151/262144, 772605/1048576]]]], [[3, 5, 4, 1, 5], [0 <
v, And(-(v^2+1)^(1/2) < u,u < -v), x = u^2-v^2-1, y < 0, (-u^2+v^2+1)^(1/2) <
z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1138531/
2097152, -569265/1048576], [-1, -1], [2, 2]]]], [[3, 9, 4, 3, 1], [0 < v, And(
v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1138531/2097152,
-569265/1048576], [1, 1], [-2, -2]]]], [[3, 9, 4, 3, 2], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/
1048576], [1, 1], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 4, 3, 3], [0
< v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, And(-(-u^2+v^2+1)^(1/
2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [-1/4194304, -1
/4194304]]]], [[3, 9, 4, 3, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = u^2-
v^2-1, 0 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [1, 1], [
193151/262144, 772605/1048576]]]], [[3, 9, 4, 3, 5], [0 < v, And(v < u,u < (v^
2+1)^(1/2)), x = u^2-v^2-1, 0 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[
1, 1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576]
, [1, 1], [2, 2]]]], [[1, 2, 4, 1, 1], [v < 0, u = -(v^2+2)^(1/2), x = 1, y <
0, z = z], [regular_chain, [[-1, -1], [-1816187/1048576, -3632373/2097152], [1
, 1], [-1, -1], [0, 0]]]], [[1, 6, 2, 3, 1], [v < 0, u = v, x = -1, 0 < y, z <
-1], [regular_chain, [[-1, -1], [-1, -1], [-1, -1], [1, 1], [-2, -2]]]], [[1,
6, 2, 3, 2], [v < 0, u = v, x = -1, 0 < y, z = -1], [regular_chain, [[-1, -1],
[-1, -1], [-1, -1], [1, 1], [-1, -1]]]], [[1, 6, 2, 3, 3], [v < 0, u = v, x =
-1, 0 < y, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [-1, -1],
[1, 1], [0, 0]]]], [[1, 6, 2, 3, 4], [v < 0, u = v, x = -1, 0 < y, z = 1], [
regular_chain, [[-1, -1], [-1, -1], [-1, -1], [1, 1], [1, 1]]]], [[1, 6, 2, 3,
5], [v < 0, u = v, x = -1, 0 < y, 1 < z], [regular_chain, [[-1, -1], [-1, -1],
[-1, -1], [1, 1], [2, 2]]]], [[2, 8, 7, 4, 1], [v = 0, u = 1, 1 < x, y = x, z
< 0], [regular_chain, [[0, 0], [1, 1], [2, 2], [2, 2], [-1, -1]]]], [[2, 8, 7,
4, 2], [v = 0, u = 1, 1 < x, y = x, z = 0], [regular_chain, [[0, 0], [1, 1], [
2, 2], [2, 2], [0, 0]]]], [[2, 8, 7, 4, 3], [v = 0, u = 1, 1 < x, y = x, 0 < z
], [regular_chain, [[0, 0], [1, 1], [2, 2], [2, 2], [1, 1]]]], [[3, 1, 5, 4, 1
], [0 < v, u < -(v^2+2)^(1/2), And(1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z =
z], [regular_chain, [[1, 1], [-3, -3], [4, 4], [3, 3], [0, 0]]]], [[3, 12, 4,
3, 1], [0 < v, u = (v^2+2)^(1/2), x = 1, 0 < y, z = z], [regular_chain, [[1, 1
], [908093/524288, 1816187/1048576], [1, 1], [1, 1], [0, 0]]]], [[1, 3, 2, 2,
1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = -1, y = -u^2+v^2,
z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-1,
-1], [-1546383/1048576, -773191/524288], [0, 0]]]], [[1, 6, 4, 5, 1], [v < 0,
u = v, x = 1, 2 < y, z < -1], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [3,
3], [-2, -2]]]], [[1, 6, 4, 5, 2], [v < 0, u = v, x = 1, 2 < y, z = -1], [
regular_chain, [[-1, -1], [-1, -1], [1, 1], [3, 3], [-1, -1]]]], [[1, 6, 4, 5,
3], [v < 0, u = v, x = 1, 2 < y, And(-1 < z,z < 1)], [regular_chain, [[-1, -1]
, [-1, -1], [1, 1], [3, 3], [0, 0]]]], [[1, 6, 4, 5, 4], [v < 0, u = v, x = 1,
2 < y, z = 1], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [3, 3], [1, 1]]]],
[[1, 6, 4, 5, 5], [v < 0, u = v, x = 1, 2 < y, 1 < z], [regular_chain, [[-1, -\
1], [-1, -1], [1, 1], [3, 3], [2, 2]]]], [[2, 8, 7, 2, 1], [v = 0, u = 1, 1 <
x, y = -x, z < 0], [regular_chain, [[0, 0], [1, 1], [2, 2], [-2, -2], [-1, -1]
]]], [[2, 8, 7, 2, 2], [v = 0, u = 1, 1 < x, y = -x, z = 0], [regular_chain, [
[0, 0], [1, 1], [2, 2], [-2, -2], [0, 0]]]], [[2, 8, 7, 2, 3], [v = 0, u = 1,
1 < x, y = -x, 0 < z], [regular_chain, [[0, 0], [1, 1], [2, 2], [-2, -2], [1,
1]]]], [[3, 1, 4, 3, 1], [0 < v, u < -(v^2+2)^(1/2), x = 1, And(-u^2+v^2+2 < y
,y < u^2-v^2-2), z = z], [regular_chain, [[1, 1], [-3, -3], [1, 1], [0, 0], [0
, 0]]]], [[3, 13, 2, 4, 1], [0 < v, (v^2+2)^(1/2) < u, x = -1, y = u^2-v^2, z
= z], [regular_chain, [[1, 1], [3, 3], [-1, -1], [8, 8], [0, 0]]]], [[1, 10, 4
, 1, 1], [v < 0, u = (v^2+1)^(1/2), x = 0, y < 0, z < 0], [regular_chain, [[-1
, -1], [741455/524288, 1482911/1048576], [0, 0], [-1, -1], [-1, -1]]]], [[1, 
10, 4, 1, 2], [v < 0, u = (v^2+1)^(1/2), x = 0, y < 0, z = 0], [regular_chain,
[[-1, -1], [741455/524288, 1482911/1048576], [0, 0], [-1, -1], [0, 0]]]], [[1,
10, 4, 1, 3], [v < 0, u = (v^2+1)^(1/2), x = 0, y < 0, 0 < z], [regular_chain,
[[-1, -1], [741455/524288, 1482911/1048576], [0, 0], [-1, -1], [1, 1]]]], [[2,
1, 1, 4, 1], [v = 0, u < -2^(1/2), x < -1, y = u^2-x-1, z = z], [regular_chain
, [[0, 0], [-3, -3], [-2, -2], [10, 10], [0, 0]]]], [[3, 5, 2, 1, 1], [0 < v,
And(-(v^2+1)^(1/2) < u,u < -v), x = -1, y < -u^2+v^2, z < -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-2
, -2], [-2, -2]]]], [[3, 5, 2, 1, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
x = -1, y < -u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [-1, -1], [-2, -2], [-772605/1048576, -\
1545209/2097152]]]], [[3, 5, 2, 1, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
x = -1, y < -u^2+v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-2, -\
2], [-1/4194304, -1/4194304]]]], [[3, 5, 2, 1, 4], [0 < v, And(-(v^2+1)^(1/2)
< u,u < -v), x = -1, y < -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-2, -2], [193151/
262144, 772605/1048576]]]], [[3, 5, 2, 1, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u
< -v), x = -1, y < -u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1],
[-1265743/1048576, -1265743/1048576], [-1, -1], [-2, -2], [2, 2]]]], [[3, 9, 1
, 4, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z < -(
-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576
], [-2, -2], [763943/524288, 1527887/1048576], [-2, -2]]]], [[3, 9, 1, 4, 2],
[0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -\
2], [763943/524288, 1527887/1048576], [-772605/1048576, -1545209/2097152]]]],
[[3, 9, 1, 4, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-\
1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1,
1], [1265743/1048576, 1265743/1048576], [-2, -2], [763943/524288, 1527887/
1048576], [-1/4194304, -1/4194304]]]], [[3, 9, 1, 4, 4], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [763943/
524288, 1527887/1048576], [193151/262144, 772605/1048576]]]], [[3, 9, 1, 4, 5]
, [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, (-u^2+v^2+1)^
(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2,
-2], [763943/524288, 1527887/1048576], [2, 2]]]], [[1, 3, 2, 1, 1], [v < 0, 
And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = -1, y < -u^2+v^2, z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-1, -1], [-3,
-3], [0, 0]]]], [[1, 6, 4, 4, 1], [v < 0, u = v, x = 1, y = 2, z < -1], [
regular_chain, [[-1, -1], [-1, -1], [1, 1], [2, 2], [-2, -2]]]], [[1, 6, 4, 4,
2], [v < 0, u = v, x = 1, y = 2, z = -1], [regular_chain, [[-1, -1], [-1, -1],
[1, 1], [2, 2], [-1, -1]]]], [[1, 6, 4, 4, 3], [v < 0, u = v, x = 1, y = 2, 
And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [2, 2], [0, 0
]]]], [[1, 6, 4, 4, 4], [v < 0, u = v, x = 1, y = 2, z = 1], [regular_chain, [
[-1, -1], [-1, -1], [1, 1], [2, 2], [1, 1]]]], [[1, 6, 4, 4, 5], [v < 0, u = v
, x = 1, y = 2, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [2, 2], [
2, 2]]]], [[2, 8, 7, 3, 1], [v = 0, u = 1, 1 < x, And(-x < y,y < x), z < 0], [
regular_chain, [[0, 0], [1, 1], [2, 2], [0, 0], [-1, -1]]]], [[2, 8, 7, 3, 2],
[v = 0, u = 1, 1 < x, And(-x < y,y < x), z = 0], [regular_chain, [[0, 0], [1,
1], [2, 2], [0, 0], [0, 0]]]], [[2, 8, 7, 3, 3], [v = 0, u = 1, 1 < x, And(-x
< y,y < x), 0 < z], [regular_chain, [[0, 0], [1, 1], [2, 2], [0, 0], [1, 1]]]]
, [[3, 1, 4, 4, 1], [0 < v, u < -(v^2+2)^(1/2), x = 1, y = u^2-v^2-2, z = z],
[regular_chain, [[1, 1], [-3, -3], [1, 1], [6, 6], [0, 0]]]], [[3, 13, 2, 3, 1
], [0 < v, (v^2+2)^(1/2) < u, x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z = z], [
regular_chain, [[1, 1], [3, 3], [-1, -1], [0, 0], [0, 0]]]], [[1, 10, 3, 5, 1]
, [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0), -x < y, z < 0], [regular_chain
, [[-1, -1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [2, 2], [-1, -1]]
]], [[1, 10, 3, 5, 2], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0), -x < y, z
= 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1/2, -1/2
], [2, 2], [0, 0]]]], [[1, 10, 3, 5, 3], [v < 0, u = (v^2+1)^(1/2), And(-1 < x
,x < 0), -x < y, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [-1/2, -1/2], [2, 2], [1, 1]]]], [[2, 1, 1, 3, 1], [v = 0, u < -2^(1
/2), x < -1, And(x-u^2+1 < y,y < u^2-x-1), z = z], [regular_chain, [[0, 0], [-\
3, -3], [-2, -2], [0, 0], [0, 0]]]], [[3, 5, 2, 2, 1], [0 < v, And(-(v^2+1)^(1
/2) < u,u < -v), x = -1, y = -u^2+v^2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [-2, -2]]]], [[3, 5, 2, 2, 2], [0 < v, And(-(
v^2+1)^(1/2) < u,u < -v), x = -1, y = -u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [-772605/1048576, -1545209/2097152]]]], [[3,
5, 2, 2, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, y = -u^2+v^2, And
(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [-1, -1], [-479311/1048576, -239655/524288
], [-1/4194304, -1/4194304]]]], [[3, 5, 2, 2, 4], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), x = -1, y = -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-479311/1048576, -239655/
524288], [193151/262144, 772605/1048576]]]], [[3, 5, 2, 2, 5], [0 < v, And(-(v
^2+1)^(1/2) < u,u < -v), x = -1, y = -u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [2, 2]]]], [[3, 9, 1, 5, 1], [0 < v, And(v <
u,u < (v^2+1)^(1/2)), x < -1, u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [3, 3],
[-2, -2]]]], [[3, 9, 1, 5, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, u
^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-2, -2], [3, 3], [-772605/1048576, -1545209/
2097152]]]], [[3, 9, 1, 5, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, u
^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [3, 3],
[-1/4194304, -1/4194304]]]], [[3, 9, 1, 5, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), x < -1, u^2-v^2-x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [1265743/1048576, 1265743/1048576], [-2, -2], [3, 3], [193151/262144, 
772605/1048576]]]], [[3, 9, 1, 5, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x
< -1, u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [-2, -2], [3, 3], [2, 2]]]], [[1, 3, 1, 5,
1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, u^2-v^2-x-1 <
y, z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-\
2, -2], [4, 4], [0, 0]]]], [[1, 6, 5, 2, 1], [v < 0, u = v, 1 < x, y = -1-x, z
< -1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [-3, -3], [-2, -2]]]], [[1
, 6, 5, 2, 2], [v < 0, u = v, 1 < x, y = -1-x, z = -1], [regular_chain, [[-1,
-1], [-1, -1], [2, 2], [-3, -3], [-1, -1]]]], [[1, 6, 5, 2, 3], [v < 0, u = v,
1 < x, y = -1-x, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-1, -1], [2,
2], [-3, -3], [0, 0]]]], [[1, 6, 5, 2, 4], [v < 0, u = v, 1 < x, y = -1-x, z =
1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [-3, -3], [1, 1]]]], [[1, 6,
5, 2, 5], [v < 0, u = v, 1 < x, y = -1-x, 1 < z], [regular_chain, [[-1, -1], [
-1, -1], [2, 2], [-3, -3], [2, 2]]]], [[2, 8, 6, 5, 1], [v = 0, u = 1, x = 1,
1 < y, z < 0], [regular_chain, [[0, 0], [1, 1], [1, 1], [2, 2], [-1, -1]]]], [
[2, 8, 6, 5, 2], [v = 0, u = 1, x = 1, 1 < y, z = 0], [regular_chain, [[0, 0],
[1, 1], [1, 1], [2, 2], [0, 0]]]], [[2, 8, 6, 5, 3], [v = 0, u = 1, x = 1, 1 <
y, 0 < z], [regular_chain, [[0, 0], [1, 1], [1, 1], [2, 2], [1, 1]]]], [[3, 1,
4, 5, 1], [0 < v, u < -(v^2+2)^(1/2), x = 1, u^2-v^2-2 < y, z = z], [
regular_chain, [[1, 1], [-3, -3], [1, 1], [7, 7], [0, 0]]]], [[3, 13, 2, 2, 1]
, [0 < v, (v^2+2)^(1/2) < u, x = -1, y = -u^2+v^2, z = z], [regular_chain, [[1
, 1], [3, 3], [-1, -1], [-8, -8], [0, 0]]]], [[1, 10, 3, 4, 1], [v < 0, u = (v
^2+1)^(1/2), And(-1 < x,x < 0), y = -x, z < 0], [regular_chain, [[-1, -1], [
741455/524288, 1482911/1048576], [-1/2, -1/2], [1/2, 1/2], [-1, -1]]]], [[1, 
10, 3, 4, 2], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0), y = -x, z = 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [1/2
, 1/2], [0, 0]]]], [[1, 10, 3, 4, 3], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x
< 0), y = -x, 0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/
1048576], [-1/2, -1/2], [1/2, 1/2], [1, 1]]]], [[2, 1, 2, 1, 1], [v = 0, u < -
2^(1/2), x = -1, y < -u^2, z = z], [regular_chain, [[0, 0], [-3, -3], [-1, -1]
, [-10, -10], [0, 0]]]], [[3, 5, 1, 4, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u <
-v), x < -1, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1
], [-1265743/1048576, -1265743/1048576], [-2, -2], [763943/524288, 1527887/
1048576], [-2, -2]]]], [[3, 5, 1, 4, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v
), x < -1, y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[-1265743/1048576, -1265743/1048576], [-2, -2], [763943/524288, 1527887/
1048576], [-772605/1048576, -1545209/2097152]]]], [[3, 5, 1, 4, 3], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), x < -1, y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/
2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [-2, -2], [763943/524288, 1527887/1048576], [-1/4194304, -1/
4194304]]]], [[3, 5, 1, 4, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1,
y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [763943/524288, 1527887/1048576], [
193151/262144, 772605/1048576]]]], [[3, 5, 1, 4, 5], [0 < v, And(-(v^2+1)^(1/2
) < u,u < -v), x < -1, y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-2, -2], [
763943/524288, 1527887/1048576], [2, 2]]]], [[3, 9, 2, 1, 1], [0 < v, And(v <
u,u < (v^2+1)^(1/2)), x = -1, y < -u^2+v^2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [-2, -2]
, [-2, -2]]]], [[3, 9, 2, 1, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1,
y < -u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-1, -1], [-2, -2], [-772605/1048576, -1545209/
2097152]]]], [[3, 9, 2, 1, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, y
< -u^2+v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [-2, -2]
, [-1/4194304, -1/4194304]]]], [[3, 9, 2, 1, 4], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), x = -1, y < -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1
], [1265743/1048576, 1265743/1048576], [-1, -1], [-2, -2], [193151/262144, 
772605/1048576]]]], [[3, 9, 2, 1, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x
= -1, y < -u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743
/1048576, 1265743/1048576], [-1, -1], [-2, -2], [2, 2]]]], [[1, 3, 1, 4, 1], [
v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z
= z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-2, -2
], [1297479/524288, 2594959/1048576], [0, 0]]]], [[1, 6, 5, 1, 1], [v < 0, u =
v, 1 < x, y < -1-x, z < -1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [-4,
-4], [-2, -2]]]], [[1, 6, 5, 1, 2], [v < 0, u = v, 1 < x, y < -1-x, z = -1], [
regular_chain, [[-1, -1], [-1, -1], [2, 2], [-4, -4], [-1, -1]]]], [[1, 6, 5,
1, 3], [v < 0, u = v, 1 < x, y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[-\
1, -1], [-1, -1], [2, 2], [-4, -4], [0, 0]]]], [[1, 6, 5, 1, 4], [v < 0, u = v
, 1 < x, y < -1-x, z = 1], [regular_chain, [[-1, -1], [-1, -1], [2, 2], [-4, -\
4], [1, 1]]]], [[1, 6, 5, 1, 5], [v < 0, u = v, 1 < x, y < -1-x, 1 < z], [
regular_chain, [[-1, -1], [-1, -1], [2, 2], [-4, -4], [2, 2]]]], [[2, 8, 7, 1,
1], [v = 0, u = 1, 1 < x, y < -x, z < 0], [regular_chain, [[0, 0], [1, 1], [2,
2], [-3, -3], [-1, -1]]]], [[2, 8, 7, 1, 2], [v = 0, u = 1, 1 < x, y < -x, z =
0], [regular_chain, [[0, 0], [1, 1], [2, 2], [-3, -3], [0, 0]]]], [[2, 8, 7, 1
, 3], [v = 0, u = 1, 1 < x, y < -x, 0 < z], [regular_chain, [[0, 0], [1, 1], [
2, 2], [-3, -3], [1, 1]]]], [[3, 1, 5, 1, 1], [0 < v, u < -(v^2+2)^(1/2), And(
1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-3, -\
3], [4, 4], [-4, -4], [0, 0]]]], [[3, 13, 2, 1, 1], [0 < v, (v^2+2)^(1/2) < u,
x = -1, y < -u^2+v^2, z = z], [regular_chain, [[1, 1], [3, 3], [-1, -1], [-9,
-9], [0, 0]]]], [[1, 10, 3, 3, 1], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0
), And(x < y,y < -x), z < 0], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [-1/2, -1/2], [0, 0], [-1, -1]]]], [[1, 10, 3, 3, 2], [v < 0
, u = (v^2+1)^(1/2), And(-1 < x,x < 0), And(x < y,y < -x), z = 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [-1/2, -1/2], [0,
0], [0, 0]]]], [[1, 10, 3, 3, 3], [v < 0, u = (v^2+1)^(1/2), And(-1 < x,x < 0)
, And(x < y,y < -x), 0 < z], [regular_chain, [[-1, -1], [741455/524288, 
1482911/1048576], [-1/2, -1/2], [0, 0], [1, 1]]]], [[2, 1, 1, 5, 1], [v = 0, u
< -2^(1/2), x < -1, u^2-x-1 < y, z = z], [regular_chain, [[0, 0], [-3, -3], [-\
2, -2], [11, 11], [0, 0]]]], [[3, 5, 1, 5, 1], [0 < v, And(-(v^2+1)^(1/2) < u,
u < -v), x < -1, u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [-1265743/1048576, -1265743/1048576], [-2, -2], [3, 3], [-2, -2]]]], [[
3, 5, 1, 5, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, u^2-v^2-x-1 <
y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [-2, -2], [3, 3], [-772605/1048576, -1545209/2097152]]]], [[
3, 5, 1, 5, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, u^2-v^2-x-1 <
y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1,
1], [-1265743/1048576, -1265743/1048576], [-2, -2], [3, 3], [-1/4194304, -1/
4194304]]]], [[3, 5, 1, 5, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1,
u^2-v^2-x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [3, 3], [193151/262144, 772605/1048576]]
]], [[3, 5, 1, 5, 5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x < -1, u^2-v^2-
x-1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576,
-1265743/1048576], [-2, -2], [3, 3], [2, 2]]]], [[3, 9, 2, 2, 1], [0 < v, And(
v < u,u < (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [-479311
/1048576, -239655/524288], [-2, -2]]]], [[3, 9, 2, 2, 2], [0 < v, And(v < u,u
< (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [-479311
/1048576, -239655/524288], [-772605/1048576, -1545209/2097152]]]], [[3, 9, 2,
2, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, And(-(-u^2+
v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-1, -1], [-479311/1048576, -239655/524288], [-1/
4194304, -1/4194304]]]], [[3, 9, 2, 2, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)
), x = -1, y = -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [-1, -1], [-479311/1048576, -239655/524288]
, [193151/262144, 772605/1048576]]]], [[3, 9, 2, 2, 5], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x = -1, y = -u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [-479311/1048576, -\
239655/524288], [2, 2]]]], [[1, 10, 5, 2, 1], [v < 0, u = (v^2+1)^(1/2), And(0
< x,x < 1), y = -x, z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911
/1048576], [1/2, 1/2], [-1/2, -1/2], [-1, -1]]]], [[1, 10, 5, 2, 2], [v < 0, u
= (v^2+1)^(1/2), And(0 < x,x < 1), y = -x, z = 0], [regular_chain, [[-1, -1],
[741455/524288, 1482911/1048576], [1/2, 1/2], [-1/2, -1/2], [0, 0]]]], [[1, 10
, 5, 2, 3], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1), y = -x, 0 < z], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1/2, 1/2], [-1/2,
-1/2], [1, 1]]]], [[2, 1, 2, 3, 1], [v = 0, u < -2^(1/2), x = -1, And(-u^2 < y
,y < u^2), z = z], [regular_chain, [[0, 0], [-3, -3], [-1, -1], [0, 0], [0, 0]
]]], [[3, 5, 2, 5, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, u^2-v^2
< y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [-1, -1], [2, 2], [-2, -2]]]], [[3, 5, 2, 5, 2], [0 < v, And
(-(v^2+1)^(1/2) < u,u < -v), x = -1, u^2-v^2 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [2, 2]
, [-772605/1048576, -1545209/2097152]]]], [[3, 5, 2, 5, 3], [0 < v, And(-(v^2+
1)^(1/2) < u,u < -v), x = -1, u^2-v^2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u
^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-1, -1], [2, 2], [-1/4194304, -1/4194304]]]], [[3, 5, 2, 5, 4], [0
< v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, u^2-v^2 < y, z = (-u^2+v^2+1)^(1/
2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1],
[2, 2], [193151/262144, 772605/1048576]]]], [[3, 5, 2, 5, 5], [0 < v, And(-(v^
2+1)^(1/2) < u,u < -v), x = -1, u^2-v^2 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [2, 2]
, [2, 2]]]], [[3, 9, 2, 3, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, 
And(-u^2+v^2 < y,y < u^2-v^2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [1265743/1048576, 1265743/1048576], [-1, -1], [0, 0], [-2, -2]]]], [[3, 9,
2, 3, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u
^2-v^2), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576,
1265743/1048576], [-1, -1], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[
3, 9, 2, 3, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y
,y < u^2-v^2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [0, 0],
[-1/4194304, -1/4194304]]]], [[3, 9, 2, 3, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [0, 0],
[193151/262144, 772605/1048576]]]], [[3, 9, 2, 3, 5], [0 < v, And(v < u,u < (v
^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), (-u^2+v^2+1)^(1/2) < z],
[regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [0, 0],
[2, 2]]]], [[1, 3, 1, 3, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)
), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[-1,
-1], [-6598195/4194304, -6598195/4194304], [-2, -2], [0, 0], [0, 0]]]], [[1, 6
, 4, 1, 1], [v < 0, u = v, x = 1, y < -2, z < -1], [regular_chain, [[-1, -1],
[-1, -1], [1, 1], [-3, -3], [-2, -2]]]], [[1, 6, 4, 1, 2], [v < 0, u = v, x =
1, y < -2, z = -1], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [-3, -3], [-1
, -1]]]], [[1, 6, 4, 1, 3], [v < 0, u = v, x = 1, y < -2, And(-1 < z,z < 1)],
[regular_chain, [[-1, -1], [-1, -1], [1, 1], [-3, -3], [0, 0]]]], [[1, 6, 4, 1
, 4], [v < 0, u = v, x = 1, y < -2, z = 1], [regular_chain, [[-1, -1], [-1, -1
], [1, 1], [-3, -3], [1, 1]]]], [[1, 6, 4, 1, 5], [v < 0, u = v, x = 1, y < -2
, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [-3, -3], [2, 2]]]], [[
2, 8, 6, 3, 1], [v = 0, u = 1, x = 1, And(-1 < y,y < 1), z < 0], [
regular_chain, [[0, 0], [1, 1], [1, 1], [0, 0], [-1, -1]]]], [[2, 8, 6, 3, 2],
[v = 0, u = 1, x = 1, And(-1 < y,y < 1), z = 0], [regular_chain, [[0, 0], [1,
1], [1, 1], [0, 0], [0, 0]]]], [[2, 8, 6, 3, 3], [v = 0, u = 1, x = 1, And(-1
< y,y < 1), 0 < z], [regular_chain, [[0, 0], [1, 1], [1, 1], [0, 0], [1, 1]]]]
, [[3, 1, 3, 4, 1], [0 < v, u < -(v^2+2)^(1/2), And(-1 < x,x < 1), y = u^2-v^2
-x-1, z = z], [regular_chain, [[1, 1], [-3, -3], [0, 0], [7, 7], [0, 0]]]], [[
3, 13, 1, 5, 1], [0 < v, (v^2+2)^(1/2) < u, x < -1, u^2-v^2-x-1 < y, z = z], [
regular_chain, [[1, 1], [3, 3], [-2, -2], [10, 10], [0, 0]]]], [[1, 10, 5, 1,
1], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1), y < -x, z < 0], [
regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [1/2, 1/2], [-2, -\
2], [-1, -1]]]], [[1, 10, 5, 1, 2], [v < 0, u = (v^2+1)^(1/2), And(0 < x,x < 1
), y < -x, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576]
, [1/2, 1/2], [-2, -2], [0, 0]]]], [[1, 10, 5, 1, 3], [v < 0, u = (v^2+1)^(1/2
), And(0 < x,x < 1), y < -x, 0 < z], [regular_chain, [[-1, -1], [741455/524288
, 1482911/1048576], [1/2, 1/2], [-2, -2], [1, 1]]]], [[2, 1, 2, 2, 1], [v = 0,
u < -2^(1/2), x = -1, y = -u^2, z = z], [regular_chain, [[0, 0], [-3, -3], [-1
, -1], [-9, -9], [0, 0]]]], [[3, 5, 3, 1, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u
< -v), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/
4194304, -3235683/4194304], [-2, -2], [-2, -2]]]], [[3, 5, 3, 1, 2], [0 < v, 
And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z
= -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-772605/1048576, -\
1545209/2097152]]]], [[3, 5, 3, 1, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-
u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-1/4194304, -1/
4194304]]]], [[3, 5, 3, 1, 4], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1
< x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [-1265743/1048576, -1265743/1048576], [-3235683/4194304, -3235683/
4194304], [-2, -2], [193151/262144, 772605/1048576]]]], [[3, 5, 3, 1, 5], [0 <
v, And(-(v^2+1)^(1/2) < u,u < -v), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1,
(-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [2, 2]]]], [[3, 9, 2
, 4, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, y = u^2-v^2, z < -(-u^2
+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [
-1, -1], [239655/524288, 479311/1048576], [-2, -2]]]], [[3, 9, 2, 4, 2], [0 <
v, And(v < u,u < (v^2+1)^(1/2)), x = -1, y = u^2-v^2, z = -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [
239655/524288, 479311/1048576], [-772605/1048576, -1545209/2097152]]]], [[3, 9
, 2, 4, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, y = u^2-v^2, And(-(-
u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [-1, -1], [239655/524288, 479311/1048576],
[-1/4194304, -1/4194304]]]], [[3, 9, 2, 4, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), x = -1, y = u^2-v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [-1, -1], [239655/524288, 479311/1048576],
[193151/262144, 772605/1048576]]]], [[3, 9, 2, 4, 5], [0 < v, And(v < u,u < (v
^2+1)^(1/2)), x = -1, y = u^2-v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[
1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [239655/524288, 479311/
1048576], [2, 2]]]], [[1, 3, 1, 2, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^
2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [-\
6598195/4194304, -6598195/4194304], [-2, -2], [-2594959/1048576, -1297479/
524288], [0, 0]]]], [[1, 6, 3, 5, 1], [v < 0, u = v, And(-1 < x,x < 1), x+1 <
y, z < -1], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [2, 2], [-2, -2]]]],
[[1, 6, 3, 5, 2], [v < 0, u = v, And(-1 < x,x < 1), x+1 < y, z = -1], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [2, 2], [-1, -1]]]], [[1, 6, 3, 5,
3], [v < 0, u = v, And(-1 < x,x < 1), x+1 < y, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [0, 0], [2, 2], [0, 0]]]], [[1, 6, 3, 5, 4
], [v < 0, u = v, And(-1 < x,x < 1), x+1 < y, z = 1], [regular_chain, [[-1, -1
], [-1, -1], [0, 0], [2, 2], [1, 1]]]], [[1, 6, 3, 5, 5], [v < 0, u = v, And(-\
1 < x,x < 1), x+1 < y, 1 < z], [regular_chain, [[-1, -1], [-1, -1], [0, 0], [2
, 2], [2, 2]]]], [[2, 8, 6, 4, 1], [v = 0, u = 1, x = 1, y = 1, z < 0], [
regular_chain, [[0, 0], [1, 1], [1, 1], [1, 1], [-1, -1]]]], [[2, 8, 6, 4, 2],
[v = 0, u = 1, x = 1, y = 1, z = 0], [regular_chain, [[0, 0], [1, 1], [1, 1],
[1, 1], [0, 0]]]], [[2, 8, 6, 4, 3], [v = 0, u = 1, x = 1, y = 1, 0 < z], [
regular_chain, [[0, 0], [1, 1], [1, 1], [1, 1], [1, 1]]]], [[3, 1, 3, 5, 1], [
0 < v, u < -(v^2+2)^(1/2), And(-1 < x,x < 1), u^2-v^2-x-1 < y, z = z], [
regular_chain, [[1, 1], [-3, -3], [0, 0], [8, 8], [0, 0]]]], [[3, 13, 1, 4, 1]
, [0 < v, (v^2+2)^(1/2) < u, x < -1, y = u^2-v^2-x-1, z = z], [regular_chain,
[[1, 1], [3, 3], [-2, -2], [9, 9], [0, 0]]]], [[1, 10, 4, 3, 1], [v < 0, u = (
v^2+1)^(1/2), x = 0, 0 < y, z < 0], [regular_chain, [[-1, -1], [741455/524288,
1482911/1048576], [0, 0], [1, 1], [-1, -1]]]], [[1, 10, 4, 3, 2], [v < 0, u =
(v^2+1)^(1/2), x = 0, 0 < y, z = 0], [regular_chain, [[-1, -1], [741455/524288
, 1482911/1048576], [0, 0], [1, 1], [0, 0]]]], [[1, 10, 4, 3, 3], [v < 0, u =
(v^2+1)^(1/2), x = 0, 0 < y, 0 < z], [regular_chain, [[-1, -1], [741455/524288
, 1482911/1048576], [0, 0], [1, 1], [1, 1]]]], [[2, 1, 2, 5, 1], [v = 0, u < -
2^(1/2), x = -1, u^2 < y, z = z], [regular_chain, [[0, 0], [-3, -3], [-1, -1],
[10, 10], [0, 0]]]], [[3, 5, 2, 3, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v),
x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [0, 0]
, [-2, -2]]]], [[3, 5, 2, 3, 2], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = -\
1, And(-u^2+v^2 < y,y < u^2-v^2), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [0, 0], [-772605/
1048576, -1545209/2097152]]]], [[3, 5, 2, 3, 3], [0 < v, And(-(v^2+1)^(1/2) <
u,u < -v), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), And(-(-u^2+v^2+1)^(1/2) < z,
z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-1265743/1048576, -1265743
/1048576], [-1, -1], [0, 0], [-1/4194304, -1/4194304]]]], [[3, 5, 2, 3, 4], [0
< v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z
= (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/
1048576], [-1, -1], [0, 0], [193151/262144, 772605/1048576]]]], [[3, 5, 2, 3,
5], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, And(-u^2+v^2 < y,y < u^2-v
^2), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [-1265743/1048576, -\
1265743/1048576], [-1, -1], [0, 0], [2, 2]]]], [[3, 9, 2, 5, 1], [0 < v, And(v
< u,u < (v^2+1)^(1/2)), x = -1, u^2-v^2 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [2, 2],
[-2, -2]]]], [[3, 9, 2, 5, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, u
^2-v^2 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-1, -1], [2, 2], [-772605/1048576, -1545209/
2097152]]]], [[3, 9, 2, 5, 3], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, u
^2-v^2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-1, -1], [2, 2],
[-1/4194304, -1/4194304]]]], [[3, 9, 2, 5, 4], [0 < v, And(v < u,u < (v^2+1)^(
1/2)), x = -1, u^2-v^2 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[1265743/1048576, 1265743/1048576], [-1, -1], [2, 2], [193151/262144, 772605/
1048576]]]], [[3, 9, 2, 5, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x = -1, u
^2-v^2 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576
, 1265743/1048576], [-1, -1], [2, 2], [2, 2]]]], [[1, 3, 1, 1, 1], [v < 0, And
(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-2, -2], [-4,
-4], [0, 0]]]], [[1, 6, 4, 3, 1], [v < 0, u = v, x = 1, And(-2 < y,y < 2), z <
-1], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [0, 0], [-2, -2]]]], [[1, 6,
4, 3, 2], [v < 0, u = v, x = 1, And(-2 < y,y < 2), z = -1], [regular_chain, [[
-1, -1], [-1, -1], [1, 1], [0, 0], [-1, -1]]]], [[1, 6, 4, 3, 3], [v < 0, u =
v, x = 1, And(-2 < y,y < 2), And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [-\
1, -1], [1, 1], [0, 0], [0, 0]]]], [[1, 6, 4, 3, 4], [v < 0, u = v, x = 1, And
(-2 < y,y < 2), z = 1], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [0, 0], [
1, 1]]]], [[1, 6, 4, 3, 5], [v < 0, u = v, x = 1, And(-2 < y,y < 2), 1 < z], [
regular_chain, [[-1, -1], [-1, -1], [1, 1], [0, 0], [2, 2]]]], [[2, 8, 6, 1, 1
], [v = 0, u = 1, x = 1, y < -1, z < 0], [regular_chain, [[0, 0], [1, 1], [1,
1], [-2, -2], [-1, -1]]]], [[2, 8, 6, 1, 2], [v = 0, u = 1, x = 1, y < -1, z =
0], [regular_chain, [[0, 0], [1, 1], [1, 1], [-2, -2], [0, 0]]]], [[2, 8, 6, 1
, 3], [v = 0, u = 1, x = 1, y < -1, 0 < z], [regular_chain, [[0, 0], [1, 1], [
1, 1], [-2, -2], [1, 1]]]], [[3, 1, 4, 1, 1], [0 < v, u < -(v^2+2)^(1/2), x =
1, y < -u^2+v^2+2, z = z], [regular_chain, [[1, 1], [-3, -3], [1, 1], [-7, -7]
, [0, 0]]]], [[3, 13, 1, 3, 1], [0 < v, (v^2+2)^(1/2) < u, x < -1, And(x-u^2+v
^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[1, 1], [3, 3], [-2, -2],
[0, 0], [0, 0]]]], [[1, 10, 4, 2, 1], [v < 0, u = (v^2+1)^(1/2), x = 0, y = 0,
z < 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [0, 0], [
0, 0], [-1, -1]]]], [[1, 10, 4, 2, 2], [v < 0, u = (v^2+1)^(1/2), x = 0, y = 0
, z = 0], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [0, 0],
[0, 0], [0, 0]]]], [[1, 10, 4, 2, 3], [v < 0, u = (v^2+1)^(1/2), x = 0, y = 0,
0 < z], [regular_chain, [[-1, -1], [741455/524288, 1482911/1048576], [0, 0], [
0, 0], [1, 1]]]], [[2, 1, 2, 4, 1], [v = 0, u < -2^(1/2), x = -1, y = u^2, z =
z], [regular_chain, [[0, 0], [-3, -3], [-1, -1], [9, 9], [0, 0]]]], [[3, 5, 2,
4, 1], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, y = u^2-v^2, z < -(-u^2
+v^2+1)^(1/2)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576],
[-1, -1], [239655/524288, 479311/1048576], [-2, -2]]]], [[3, 5, 2, 4, 2], [0 <
v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, y = u^2-v^2, z = -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [
239655/524288, 479311/1048576], [-772605/1048576, -1545209/2097152]]]], [[3, 5
, 2, 4, 3], [0 < v, And(-(v^2+1)^(1/2) < u,u < -v), x = -1, y = u^2-v^2, And(-
(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [-\
1265743/1048576, -1265743/1048576], [-1, -1], [239655/524288, 479311/1048576],
[-1/4194304, -1/4194304]]]], [[3, 5, 2, 4, 4], [0 < v, And(-(v^2+1)^(1/2) < u,
u < -v), x = -1, y = u^2-v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [-1265743/1048576, -1265743/1048576], [-1, -1], [239655/524288, 479311/
1048576], [193151/262144, 772605/1048576]]]], [[3, 5, 2, 4, 5], [0 < v, And(-(
v^2+1)^(1/2) < u,u < -v), x = -1, y = u^2-v^2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [-1265743/1048576, -1265743/1048576], [-1, -1], [
239655/524288, 479311/1048576], [2, 2]]]], [[3, 9, 3, 1, 1], [0 < v, And(v < u
,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z < -(-u^2+v^
2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-\
3235683/4194304, -3235683/4194304], [-2, -2], [-2, -2]]]], [[3, 9, 3, 1, 2], [
0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+
1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-772605/
1048576, -1545209/2097152]]]], [[3, 9, 3, 1, 3], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) <
z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743
/1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-1/4194304, -1/
4194304]]]], [[3, 9, 3, 1, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), And(-1 <
x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304
], [-2, -2], [193151/262144, 772605/1048576]]]], [[3, 9, 3, 1, 5], [0 < v, And
(v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, (-u^2+v
^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576],
[-3235683/4194304, -3235683/4194304], [-2, -2], [2, 2]]]], [[1, 2, 5, 5, 1], [
v < 0, u = -(v^2+2)^(1/2), 1 < x, x-1 < y, z = z], [regular_chain, [[-1, -1],
[-1816187/1048576, -3632373/2097152], [2, 2], [2, 2], [0, 0]]]], [[1, 6, 4, 2,
1], [v < 0, u = v, x = 1, y = -2, z < -1], [regular_chain, [[-1, -1], [-1, -1]
, [1, 1], [-2, -2], [-2, -2]]]], [[1, 6, 4, 2, 2], [v < 0, u = v, x = 1, y = -\
2, z = -1], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [-2, -2], [-1, -1]]]]
, [[1, 6, 4, 2, 3], [v < 0, u = v, x = 1, y = -2, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [-1, -1], [1, 1], [-2, -2], [0, 0]]]], [[1, 6, 4, 2,
4], [v < 0, u = v, x = 1, y = -2, z = 1], [regular_chain, [[-1, -1], [-1, -1],
[1, 1], [-2, -2], [1, 1]]]], [[1, 6, 4, 2, 5], [v < 0, u = v, x = 1, y = -2, 1
< z], [regular_chain, [[-1, -1], [-1, -1], [1, 1], [-2, -2], [2, 2]]]], [[2, 8
, 6, 2, 1], [v = 0, u = 1, x = 1, y = -1, z < 0], [regular_chain, [[0, 0], [1,
1], [1, 1], [-1, -1], [-1, -1]]]], [[2, 8, 6, 2, 2], [v = 0, u = 1, x = 1, y =
-1, z = 0], [regular_chain, [[0, 0], [1, 1], [1, 1], [-1, -1], [0, 0]]]], [[2,
8, 6, 2, 3], [v = 0, u = 1, x = 1, y = -1, 0 < z], [regular_chain, [[0, 0], [1
, 1], [1, 1], [-1, -1], [1, 1]]]], [[3, 1, 4, 2, 1], [0 < v, u < -(v^2+2)^(1/2
), x = 1, y = -u^2+v^2+2, z = z], [regular_chain, [[1, 1], [-3, -3], [1, 1], [
-6, -6], [0, 0]]]], [[3, 13, 1, 2, 1], [0 < v, (v^2+2)^(1/2) < u, x < -1, y =
x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [3, 3], [-2, -2], [-9, -9], [0,
0]]]], [[1, 13, 2, 4, 1], [v < 0, (v^2+2)^(1/2) < u, x = -1, y = u^2-v^2, z =
z], [regular_chain, [[-1, -1], [3, 3], [-1, -1], [8, 8], [0, 0]]]], [[2, 4, 7,
5, 1], [v = 0, u = -1, 1 < x, x < y, z < 0], [regular_chain, [[0, 0], [-1, -1]
, [2, 2], [3, 3], [-1, -1]]]], [[2, 4, 7, 5, 2], [v = 0, u = -1, 1 < x, x < y,
z = 0], [regular_chain, [[0, 0], [-1, -1], [2, 2], [3, 3], [0, 0]]]], [[2, 4,
7, 5, 3], [v = 0, u = -1, 1 < x, x < y, 0 < z], [regular_chain, [[0, 0], [-1,
-1], [2, 2], [3, 3], [1, 1]]]], [[3, 3, 6, 3, 1], [0 < v, And(-(v^2+2)^(1/2) <
u,u < -(v^2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [1, 1], [-1/
4194304, -1/4194304], [0, 0]]]], [[3, 8, 4, 4, 1], [0 < v, u = v, x = 1, y = 2
, z < -1], [regular_chain, [[1, 1], [1, 1], [1, 1], [2, 2], [-2, -2]]]], [[3,
8, 4, 4, 2], [0 < v, u = v, x = 1, y = 2, z = -1], [regular_chain, [[1, 1], [1
, 1], [1, 1], [2, 2], [-1, -1]]]], [[3, 8, 4, 4, 3], [0 < v, u = v, x = 1, y =
2, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [1, 1], [2, 2], [0, 0]
]]], [[3, 8, 4, 4, 4], [0 < v, u = v, x = 1, y = 2, z = 1], [regular_chain, [[
1, 1], [1, 1], [1, 1], [2, 2], [1, 1]]]], [[3, 8, 4, 4, 5], [0 < v, u = v, x =
1, y = 2, 1 < z], [regular_chain, [[1, 1], [1, 1], [1, 1], [2, 2], [2, 2]]]],
[[1, 3, 4, 2, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = u^2-
v^2-1, y = 0, z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/
4194304], [248903/524288, 497807/1048576], [0, 0], [0, 0]]]], [[1, 8, 2, 3, 1]
, [v < 0, u = -v, x = -1, 0 < y, z < -1], [regular_chain, [[-1, -1], [1, 1], [
-1, -1], [1, 1], [-2, -2]]]], [[1, 8, 2, 3, 2], [v < 0, u = -v, x = -1, 0 < y,
z = -1], [regular_chain, [[-1, -1], [1, 1], [-1, -1], [1, 1], [-1, -1]]]], [[1
, 8, 2, 3, 3], [v < 0, u = -v, x = -1, 0 < y, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [1, 1], [-1, -1], [1, 1], [0, 0]]]], [[1, 8, 2, 3, 4
], [v < 0, u = -v, x = -1, 0 < y, z = 1], [regular_chain, [[-1, -1], [1, 1], [
-1, -1], [1, 1], [1, 1]]]], [[1, 8, 2, 3, 5], [v < 0, u = -v, x = -1, 0 < y, 1
< z], [regular_chain, [[-1, -1], [1, 1], [-1, -1], [1, 1], [2, 2]]]], [[2, 5,
1, 1, 1], [v = 0, And(-1 < u,u < 0), x < -1, y < x-u^2+1, z < -(-u^2+1)^(1/2)]
, [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-3, -3], [-2, -2]]]], [[2,
5, 1, 1, 2], [v = 0, And(-1 < u,u < 0), x < -1, y < x-u^2+1, z = -(-u^2+1)^(1/
2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-3, -3], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 1, 1, 3], [v = 0, And(-1 < u,u < 0), x
< -1, y < x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-3, -3], [-1/8388608, -1/
8388608]]]], [[2, 5, 1, 1, 4], [v = 0, And(-1 < u,u < 0), x < -1, y < x-u^2+1,
z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-3, -3]
, [908093/1048576, 454047/524288]]]], [[2, 5, 1, 1, 5], [v = 0, And(-1 < u,u <
0), x < -1, y < x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2,
-1/2], [-2, -2], [-3, -3], [2, 2]]]], [[2, 9, 6, 2, 1], [v = 0, And(1 < u,u <
2^(1/2)), x = 1, y = u^2-2, z = z], [regular_chain, [[0, 0], [1265743/1048576,
1265743/1048576], [1, 1], [-1138531/2097152, -569265/1048576], [0, 0]]]], [[3,
13, 4, 4, 1], [0 < v, (v^2+2)^(1/2) < u, x = 1, y = u^2-v^2-2, z = z], [
regular_chain, [[1, 1], [3, 3], [1, 1], [6, 6], [0, 0]]]], [[1, 13, 2, 3, 1],
[v < 0, (v^2+2)^(1/2) < u, x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z = z], [
regular_chain, [[-1, -1], [3, 3], [-1, -1], [0, 0], [0, 0]]]], [[2, 4, 7, 4, 1
], [v = 0, u = -1, 1 < x, y = x, z < 0], [regular_chain, [[0, 0], [-1, -1], [2
, 2], [2, 2], [-1, -1]]]], [[2, 4, 7, 4, 2], [v = 0, u = -1, 1 < x, y = x, z =
0], [regular_chain, [[0, 0], [-1, -1], [2, 2], [2, 2], [0, 0]]]], [[2, 4, 7, 4
, 3], [v = 0, u = -1, 1 < x, y = x, 0 < z], [regular_chain, [[0, 0], [-1, -1],
[2, 2], [2, 2], [1, 1]]]], [[3, 3, 6, 4, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u
< -(v^2+1)^(1/2)), x = 1, y = -u^2+v^2+2, z = z], [regular_chain, [[1, 1], [-\
6598195/4194304, -6598195/4194304], [1, 1], [550769/1048576, 275385/524288], [
0, 0]]]], [[3, 8, 4, 5, 1], [0 < v, u = v, x = 1, 2 < y, z < -1], [
regular_chain, [[1, 1], [1, 1], [1, 1], [3, 3], [-2, -2]]]], [[3, 8, 4, 5, 2],
[0 < v, u = v, x = 1, 2 < y, z = -1], [regular_chain, [[1, 1], [1, 1], [1, 1],
[3, 3], [-1, -1]]]], [[3, 8, 4, 5, 3], [0 < v, u = v, x = 1, 2 < y, And(-1 < z
,z < 1)], [regular_chain, [[1, 1], [1, 1], [1, 1], [3, 3], [0, 0]]]], [[3, 8,
4, 5, 4], [0 < v, u = v, x = 1, 2 < y, z = 1], [regular_chain, [[1, 1], [1, 1]
, [1, 1], [3, 3], [1, 1]]]], [[3, 8, 4, 5, 5], [0 < v, u = v, x = 1, 2 < y, 1
< z], [regular_chain, [[1, 1], [1, 1], [1, 1], [3, 3], [2, 2]]]], [[1, 3, 4, 1
, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = u^2-v^2-1, y < 0
, z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [
248903/524288, 497807/1048576], [-1, -1], [0, 0]]]], [[1, 8, 2, 2, 1], [v < 0,
u = -v, x = -1, y = 0, z < -1], [regular_chain, [[-1, -1], [1, 1], [-1, -1], [
0, 0], [-2, -2]]]], [[1, 8, 2, 2, 2], [v < 0, u = -v, x = -1, y = 0, z = -1],
[regular_chain, [[-1, -1], [1, 1], [-1, -1], [0, 0], [-1, -1]]]], [[1, 8, 2, 2
, 3], [v < 0, u = -v, x = -1, y = 0, And(-1 < z,z < 1)], [regular_chain, [[-1,
-1], [1, 1], [-1, -1], [0, 0], [0, 0]]]], [[1, 8, 2, 2, 4], [v < 0, u = -v, x
= -1, y = 0, z = 1], [regular_chain, [[-1, -1], [1, 1], [-1, -1], [0, 0], [1,
1]]]], [[1, 8, 2, 2, 5], [v < 0, u = -v, x = -1, y = 0, 1 < z], [regular_chain
, [[-1, -1], [1, 1], [-1, -1], [0, 0], [2, 2]]]], [[2, 5, 1, 2, 1], [v = 0, 
And(-1 < u,u < 0), x < -1, y = x-u^2+1, z < -(-u^2+1)^(1/2)], [regular_chain,
[[0, 0], [-1/2, -1/2], [-2, -2], [-5/4, -5/4], [-2, -2]]]], [[2, 5, 1, 2, 2],
[v = 0, And(-1 < u,u < 0), x < -1, y = x-u^2+1, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-5/4, -5/4], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 1, 2, 3], [v = 0, And(-1 < u,u < 0), x
< -1, y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-5/4, -5/4], [-1/8388608, -1/
8388608]]]], [[2, 5, 1, 2, 4], [v = 0, And(-1 < u,u < 0), x < -1, y = x-u^2+1,
z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [-5/4, -\
5/4], [908093/1048576, 454047/524288]]]], [[2, 5, 1, 2, 5], [v = 0, And(-1 < u
,u < 0), x < -1, y = x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-\
1/2, -1/2], [-2, -2], [-5/4, -5/4], [2, 2]]]], [[2, 9, 6, 3, 1], [v = 0, And(1
< u,u < 2^(1/2)), x = 1, And(u^2-2 < y,y < -u^2+2), z = z], [regular_chain, [[
0, 0], [1265743/1048576, 1265743/1048576], [1, 1], [0, 0], [0, 0]]]], [[3, 13,
4, 3, 1], [0 < v, (v^2+2)^(1/2) < u, x = 1, And(-u^2+v^2+2 < y,y < u^2-v^2-2),
z = z], [regular_chain, [[1, 1], [3, 3], [1, 1], [0, 0], [0, 0]]]], [[1, 13, 3
, 1, 1], [v < 0, (v^2+2)^(1/2) < u, And(-1 < x,x < 1), y < x-u^2+v^2+1, z = z]
, [regular_chain, [[-1, -1], [3, 3], [0, 0], [-8, -8], [0, 0]]]], [[2, 4, 7, 3
, 1], [v = 0, u = -1, 1 < x, And(-x < y,y < x), z < 0], [regular_chain, [[0, 0
], [-1, -1], [2, 2], [0, 0], [-1, -1]]]], [[2, 4, 7, 3, 2], [v = 0, u = -1, 1
< x, And(-x < y,y < x), z = 0], [regular_chain, [[0, 0], [-1, -1], [2, 2], [0,
0], [0, 0]]]], [[2, 4, 7, 3, 3], [v = 0, u = -1, 1 < x, And(-x < y,y < x), 0 <
z], [regular_chain, [[0, 0], [-1, -1], [2, 2], [0, 0], [1, 1]]]], [[3, 3, 6, 5
, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = 1, -u^2+v^2+2 <
y, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [1,
1], [2, 2], [0, 0]]]], [[3, 8, 4, 2, 1], [0 < v, u = v, x = 1, y = -2, z < -1]
, [regular_chain, [[1, 1], [1, 1], [1, 1], [-2, -2], [-2, -2]]]], [[3, 8, 4, 2
, 2], [0 < v, u = v, x = 1, y = -2, z = -1], [regular_chain, [[1, 1], [1, 1],
[1, 1], [-2, -2], [-1, -1]]]], [[3, 8, 4, 2, 3], [0 < v, u = v, x = 1, y = -2,
And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [1, 1], [-2, -2], [0, 0]]
]], [[3, 8, 4, 2, 4], [0 < v, u = v, x = 1, y = -2, z = 1], [regular_chain, [[
1, 1], [1, 1], [1, 1], [-2, -2], [1, 1]]]], [[3, 8, 4, 2, 5], [0 < v, u = v, x
= 1, y = -2, 1 < z], [regular_chain, [[1, 1], [1, 1], [1, 1], [-2, -2], [2, 2]
]]], [[1, 3, 5, 1, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And
(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = z], [regular_chain, [[-1, -1], [-\
6598195/4194304, -6598195/4194304], [1546383/2097152, 1546383/2097152], [-2, -\
2], [0, 0]]]], [[1, 8, 2, 1, 1], [v < 0, u = -v, x = -1, y < 0, z < -1], [
regular_chain, [[-1, -1], [1, 1], [-1, -1], [-1, -1], [-2, -2]]]], [[1, 8, 2,
1, 2], [v < 0, u = -v, x = -1, y < 0, z = -1], [regular_chain, [[-1, -1], [1,
1], [-1, -1], [-1, -1], [-1, -1]]]], [[1, 8, 2, 1, 3], [v < 0, u = -v, x = -1,
y < 0, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [-1, -1], [-1, -\
1], [0, 0]]]], [[1, 8, 2, 1, 4], [v < 0, u = -v, x = -1, y < 0, z = 1], [
regular_chain, [[-1, -1], [1, 1], [-1, -1], [-1, -1], [1, 1]]]], [[1, 8, 2, 1,
5], [v < 0, u = -v, x = -1, y < 0, 1 < z], [regular_chain, [[-1, -1], [1, 1],
[-1, -1], [-1, -1], [2, 2]]]], [[2, 5, 1, 3, 1], [v = 0, And(-1 < u,u < 0), x
< -1, And(x-u^2+1 < y,y < u^2-x-1), z < -(-u^2+1)^(1/2)], [regular_chain, [[0,
0], [-1/2, -1/2], [-2, -2], [0, 0], [-2, -2]]]], [[2, 5, 1, 3, 2], [v = 0, And
(-1 < u,u < 0), x < -1, And(x-u^2+1 < y,y < u^2-x-1), z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [0, 0], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 5, 1, 3, 3], [v = 0, And(-1 < u,u < 0), x < -1, And(
x-u^2+1 < y,y < u^2-x-1), And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [0, 0], [-1/8388608, -1/
8388608]]]], [[2, 5, 1, 3, 4], [v = 0, And(-1 < u,u < 0), x < -1, And(x-u^2+1
< y,y < u^2-x-1), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2],
[-2, -2], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 5, 1, 3, 5], [v = 0
, And(-1 < u,u < 0), x < -1, And(x-u^2+1 < y,y < u^2-x-1), (-u^2+1)^(1/2) < z]
, [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [0, 0], [2, 2]]]], [[2, 9,
5, 5, 1], [v = 0, And(1 < u,u < 2^(1/2)), And(u^2-1 < x,x < 1), x-u^2+1 < y, z
= z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [1527887/
2097152, 1527887/2097152], [2, 2], [0, 0]]]], [[3, 13, 5, 1, 1], [0 < v, (v^2+
2)^(1/2) < u, And(1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [3, 3], [4, 4], [-4, -4], [0, 0]]]], [[1, 13, 2, 5, 1]
, [v < 0, (v^2+2)^(1/2) < u, x = -1, u^2-v^2 < y, z = z], [regular_chain, [[-1
, -1], [3, 3], [-1, -1], [9, 9], [0, 0]]]], [[2, 4, 7, 2, 1], [v = 0, u = -1,
1 < x, y = -x, z < 0], [regular_chain, [[0, 0], [-1, -1], [2, 2], [-2, -2], [-\
1, -1]]]], [[2, 4, 7, 2, 2], [v = 0, u = -1, 1 < x, y = -x, z = 0], [
regular_chain, [[0, 0], [-1, -1], [2, 2], [-2, -2], [0, 0]]]], [[2, 4, 7, 2, 3
], [v = 0, u = -1, 1 < x, y = -x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [
2, 2], [-2, -2], [1, 1]]]], [[3, 3, 7, 1, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u
< -(v^2+1)^(1/2)), 1 < x, y < u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [-\
6598195/4194304, -6598195/4194304], [2, 2], [-3, -3], [0, 0]]]], [[3, 8, 4, 3,
1], [0 < v, u = v, x = 1, And(-2 < y,y < 2), z < -1], [regular_chain, [[1, 1],
[1, 1], [1, 1], [0, 0], [-2, -2]]]], [[3, 8, 4, 3, 2], [0 < v, u = v, x = 1, 
And(-2 < y,y < 2), z = -1], [regular_chain, [[1, 1], [1, 1], [1, 1], [0, 0], [
-1, -1]]]], [[3, 8, 4, 3, 3], [0 < v, u = v, x = 1, And(-2 < y,y < 2), And(-1
< z,z < 1)], [regular_chain, [[1, 1], [1, 1], [1, 1], [0, 0], [0, 0]]]], [[3,
8, 4, 3, 4], [0 < v, u = v, x = 1, And(-2 < y,y < 2), z = 1], [regular_chain,
[[1, 1], [1, 1], [1, 1], [0, 0], [1, 1]]]], [[3, 8, 4, 3, 5], [0 < v, u = v, x
= 1, And(-2 < y,y < 2), 1 < z], [regular_chain, [[1, 1], [1, 1], [1, 1], [0, 0
], [2, 2]]]], [[1, 3, 4, 3, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1
/2)), x = u^2-v^2-1, 0 < y, z = z], [regular_chain, [[-1, -1], [-6598195/
4194304, -6598195/4194304], [248903/524288, 497807/1048576], [1, 1], [0, 0]]]]
, [[1, 8, 1, 5, 1], [v < 0, u = -v, x < -1, -1-x < y, z < -1], [regular_chain,
[[-1, -1], [1, 1], [-2, -2], [2, 2], [-2, -2]]]], [[1, 8, 1, 5, 2], [v < 0, u
= -v, x < -1, -1-x < y, z = -1], [regular_chain, [[-1, -1], [1, 1], [-2, -2],
[2, 2], [-1, -1]]]], [[1, 8, 1, 5, 3], [v < 0, u = -v, x < -1, -1-x < y, And(-\
1 < z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [2, 2], [0, 0]]]],
[[1, 8, 1, 5, 4], [v < 0, u = -v, x < -1, -1-x < y, z = 1], [regular_chain, [[
-1, -1], [1, 1], [-2, -2], [2, 2], [1, 1]]]], [[1, 8, 1, 5, 5], [v < 0, u = -v
, x < -1, -1-x < y, 1 < z], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [2, 2
], [2, 2]]]], [[2, 5, 1, 4, 1], [v = 0, And(-1 < u,u < 0), x < -1, y = u^2-x-1
, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [5/4,
5/4], [-2, -2]]]], [[2, 5, 1, 4, 2], [v = 0, And(-1 < u,u < 0), x < -1, y = u^
2-x-1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2],
[5/4, 5/4], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 1, 4, 3], [v = 0,
And(-1 < u,u < 0), x < -1, y = u^2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(
1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [5/4, 5/4], [-1/
8388608, -1/8388608]]]], [[2, 5, 1, 4, 4], [v = 0, And(-1 < u,u < 0), x < -1,
y = u^2-x-1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-2,
-2], [5/4, 5/4], [908093/1048576, 454047/524288]]]], [[2, 5, 1, 4, 5], [v = 0,
And(-1 < u,u < 0), x < -1, y = u^2-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [
[0, 0], [-1/2, -1/2], [-2, -2], [5/4, 5/4], [2, 2]]]], [[2, 9, 6, 1, 1], [v =
0, And(1 < u,u < 2^(1/2)), x = 1, y < u^2-2, z = z], [regular_chain, [[0, 0],
[1265743/1048576, 1265743/1048576], [1, 1], [-2, -2], [0, 0]]]], [[3, 13, 4, 5
, 1], [0 < v, (v^2+2)^(1/2) < u, x = 1, u^2-v^2-2 < y, z = z], [regular_chain,
[[1, 1], [3, 3], [1, 1], [7, 7], [0, 0]]]], [[1, 3, 5, 3, 1], [v < 0, And(-(v^
2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1
< y,y < x-u^2+v^2+1), z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -\
6598195/4194304], [1546383/2097152, 1546383/2097152], [0, 0], [0, 0]]]], [[1,
8, 3, 4, 1], [v < 0, u = -v, And(-1 < x,x < 1), y = x+1, z < -1], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [1, 1], [-2, -2]]]], [[1, 8, 3, 4, 2
], [v < 0, u = -v, And(-1 < x,x < 1), y = x+1, z = -1], [regular_chain, [[-1,
-1], [1, 1], [0, 0], [1, 1], [-1, -1]]]], [[1, 8, 3, 4, 3], [v < 0, u = -v, 
And(-1 < x,x < 1), y = x+1, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [1,
1], [0, 0], [1, 1], [0, 0]]]], [[1, 8, 3, 4, 4], [v < 0, u = -v, And(-1 < x,x
< 1), y = x+1, z = 1], [regular_chain, [[-1, -1], [1, 1], [0, 0], [1, 1], [1,
1]]]], [[1, 8, 3, 4, 5], [v < 0, u = -v, And(-1 < x,x < 1), y = x+1, 1 < z], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [1, 1], [2, 2]]]], [[2, 5, 1, 5, 1],
[v = 0, And(-1 < u,u < 0), x < -1, u^2-x-1 < y, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [3, 3], [-2, -2]]]], [[2, 5, 1
, 5, 2], [v = 0, And(-1 < u,u < 0), x < -1, u^2-x-1 < y, z = -(-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [3, 3], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 5, 1, 5, 3], [v = 0, And(-1 < u,u < 0), x < -1, u^2-
x-1 < y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0]
, [-1/2, -1/2], [-2, -2], [3, 3], [-1/8388608, -1/8388608]]]], [[2, 5, 1, 5, 4
], [v = 0, And(-1 < u,u < 0), x < -1, u^2-x-1 < y, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [3, 3], [908093/1048576, 
454047/524288]]]], [[2, 5, 1, 5, 5], [v = 0, And(-1 < u,u < 0), x < -1, u^2-x-\
1 < y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [-2, -2], [
3, 3], [2, 2]]]], [[2, 9, 7, 1, 1], [v = 0, And(1 < u,u < 2^(1/2)), 1 < x, y <
u^2-x-1, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576],
[2, 2], [-3, -3], [0, 0]]]], [[3, 13, 5, 3, 1], [0 < v, (v^2+2)^(1/2) < u, And
(1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [
regular_chain, [[1, 1], [3, 3], [4, 4], [0, 0], [0, 0]]]], [[1, 13, 1, 5, 1],
[v < 0, (v^2+2)^(1/2) < u, x < -1, u^2-v^2-x-1 < y, z = z], [regular_chain, [[
-1, -1], [3, 3], [-2, -2], [10, 10], [0, 0]]]], [[2, 4, 7, 1, 1], [v = 0, u =
-1, 1 < x, y < -x, z < 0], [regular_chain, [[0, 0], [-1, -1], [2, 2], [-3, -3]
, [-1, -1]]]], [[2, 4, 7, 1, 2], [v = 0, u = -1, 1 < x, y < -x, z = 0], [
regular_chain, [[0, 0], [-1, -1], [2, 2], [-3, -3], [0, 0]]]], [[2, 4, 7, 1, 3
], [v = 0, u = -1, 1 < x, y < -x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [
2, 2], [-3, -3], [1, 1]]]], [[3, 3, 5, 4, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u
< -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [1546383/2097152
, 1546383/2097152], [275385/1048576, 137693/524288], [0, 0]]]], [[3, 8, 3, 5,
1], [0 < v, u = v, And(-1 < x,x < 1), x+1 < y, z < -1], [regular_chain, [[1, 1
], [1, 1], [0, 0], [2, 2], [-2, -2]]]], [[3, 8, 3, 5, 2], [0 < v, u = v, And(-\
1 < x,x < 1), x+1 < y, z = -1], [regular_chain, [[1, 1], [1, 1], [0, 0], [2, 2
], [-1, -1]]]], [[3, 8, 3, 5, 3], [0 < v, u = v, And(-1 < x,x < 1), x+1 < y, 
And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [0, 0], [2, 2], [0, 0]]]]
, [[3, 8, 3, 5, 4], [0 < v, u = v, And(-1 < x,x < 1), x+1 < y, z = 1], [
regular_chain, [[1, 1], [1, 1], [0, 0], [2, 2], [1, 1]]]], [[3, 8, 3, 5, 5], [
0 < v, u = v, And(-1 < x,x < 1), x+1 < y, 1 < z], [regular_chain, [[1, 1], [1,
1], [0, 0], [2, 2], [2, 2]]]], [[1, 3, 5, 2, 1], [v < 0, And(-(v^2+2)^(1/2) <
u,u < -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [1546383/
2097152, 1546383/2097152], [-137693/524288, -275385/1048576], [0, 0]]]], [[1,
8, 3, 3, 1], [v < 0, u = -v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z < -1]
, [regular_chain, [[-1, -1], [1, 1], [0, 0], [0, 0], [-2, -2]]]], [[1, 8, 3, 3
, 2], [v < 0, u = -v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z = -1], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [0, 0], [-1, -1]]]], [[1, 8, 3, 3, 3
], [v < 0, u = -v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), And(-1 < z,z < 1)
], [regular_chain, [[-1, -1], [1, 1], [0, 0], [0, 0], [0, 0]]]], [[1, 8, 3, 3,
4], [v < 0, u = -v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z = 1], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [0, 0], [1, 1]]]], [[1, 8, 3, 3, 5],
[v < 0, u = -v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), 1 < z], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [0, 0], [2, 2]]]], [[2, 5, 2, 1, 1],
[v = 0, And(-1 < u,u < 0), x = -1, y < -u^2, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [-2, -2], [-2, -2]]]], [[2, 5,
2, 1, 2], [v = 0, And(-1 < u,u < 0), x = -1, y < -u^2, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [-2, -2], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 5, 2, 1, 3], [v = 0, And(-1 < u,u < 0), x = -1, y <
-u^2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [
-1/2, -1/2], [-1, -1], [-2, -2], [-1/8388608, -1/8388608]]]], [[2, 5, 2, 1, 4]
, [v = 0, And(-1 < u,u < 0), x = -1, y < -u^2, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [-2, -2], [908093/1048576, 
454047/524288]]]], [[2, 5, 2, 1, 5], [v = 0, And(-1 < u,u < 0), x = -1, y < -u
^2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [-2,
-2], [2, 2]]]], [[2, 9, 7, 2, 1], [v = 0, And(1 < u,u < 2^(1/2)), 1 < x, y = u
^2-x-1, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [
2, 2], [-3235683/2097152, -1617841/1048576], [0, 0]]]], [[3, 13, 5, 2, 1], [0
< v, (v^2+2)^(1/2) < u, And(1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [3, 3], [4, 4], [-3, -3], [0, 0]]]], [[1, 13, 1, 4, 1]
, [v < 0, (v^2+2)^(1/2) < u, x < -1, y = u^2-v^2-x-1, z = z], [regular_chain,
[[-1, -1], [3, 3], [-2, -2], [9, 9], [0, 0]]]], [[2, 4, 6, 5, 1], [v = 0, u =
-1, x = 1, 1 < y, z < 0], [regular_chain, [[0, 0], [-1, -1], [1, 1], [2, 2], [
-1, -1]]]], [[2, 4, 6, 5, 2], [v = 0, u = -1, x = 1, 1 < y, z = 0], [
regular_chain, [[0, 0], [-1, -1], [1, 1], [2, 2], [0, 0]]]], [[2, 4, 6, 5, 3],
[v = 0, u = -1, x = 1, 1 < y, 0 < z], [regular_chain, [[0, 0], [-1, -1], [1, 1
], [2, 2], [1, 1]]]], [[3, 3, 5, 5, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v
^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [1546383/2097152
, 1546383/2097152], [2, 2], [0, 0]]]], [[3, 8, 4, 1, 1], [0 < v, u = v, x = 1,
y < -2, z < -1], [regular_chain, [[1, 1], [1, 1], [1, 1], [-3, -3], [-2, -2]]]
], [[3, 8, 4, 1, 2], [0 < v, u = v, x = 1, y < -2, z = -1], [regular_chain, [[
1, 1], [1, 1], [1, 1], [-3, -3], [-1, -1]]]], [[3, 8, 4, 1, 3], [0 < v, u = v,
x = 1, y < -2, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [1, 1], [-\
3, -3], [0, 0]]]], [[3, 8, 4, 1, 4], [0 < v, u = v, x = 1, y < -2, z = 1], [
regular_chain, [[1, 1], [1, 1], [1, 1], [-3, -3], [1, 1]]]], [[3, 8, 4, 1, 5],
[0 < v, u = v, x = 1, y < -2, 1 < z], [regular_chain, [[1, 1], [1, 1], [1, 1],
[-3, -3], [2, 2]]]], [[1, 3, 5, 5, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^
2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y, z = z], [regular_chain
, [[-1, -1], [-6598195/4194304, -6598195/4194304], [1546383/2097152, 1546383/
2097152], [2, 2], [0, 0]]]], [[1, 8, 3, 2, 1], [v < 0, u = -v, And(-1 < x,x <
1), y = -1-x, z < -1], [regular_chain, [[-1, -1], [1, 1], [0, 0], [-1, -1], [-\
2, -2]]]], [[1, 8, 3, 2, 2], [v < 0, u = -v, And(-1 < x,x < 1), y = -1-x, z =
-1], [regular_chain, [[-1, -1], [1, 1], [0, 0], [-1, -1], [-1, -1]]]], [[1, 8,
3, 2, 3], [v < 0, u = -v, And(-1 < x,x < 1), y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [-1, -1], [0, 0]]]], [[1, 8, 3, 2, 4
], [v < 0, u = -v, And(-1 < x,x < 1), y = -1-x, z = 1], [regular_chain, [[-1,
-1], [1, 1], [0, 0], [-1, -1], [1, 1]]]], [[1, 8, 3, 2, 5], [v < 0, u = -v, 
And(-1 < x,x < 1), y = -1-x, 1 < z], [regular_chain, [[-1, -1], [1, 1], [0, 0]
, [-1, -1], [2, 2]]]], [[2, 5, 2, 2, 1], [v = 0, And(-1 < u,u < 0), x = -1, y
= -u^2, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1],
[-1/4, -1/4], [-2, -2]]]], [[2, 5, 2, 2, 2], [v = 0, And(-1 < u,u < 0), x = -1
, y = -u^2, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1,
-1], [-1/4, -1/4], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 2, 2, 3],
[v = 0, And(-1 < u,u < 0), x = -1, y = -u^2, And(-(-u^2+1)^(1/2) < z,z < (-u^2
+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [-1/4, -1/4], [-\
1/8388608, -1/8388608]]]], [[2, 5, 2, 2, 4], [v = 0, And(-1 < u,u < 0), x = -1
, y = -u^2, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -\
1], [-1/4, -1/4], [908093/1048576, 454047/524288]]]], [[2, 5, 2, 2, 5], [v = 0
, And(-1 < u,u < 0), x = -1, y = -u^2, (-u^2+1)^(1/2) < z], [regular_chain, [[
0, 0], [-1/2, -1/2], [-1, -1], [-1/4, -1/4], [2, 2]]]], [[2, 9, 6, 4, 1], [v =
0, And(1 < u,u < 2^(1/2)), x = 1, y = -u^2+2, z = z], [regular_chain, [[0, 0],
[1265743/1048576, 1265743/1048576], [1, 1], [569265/1048576, 284633/524288], [
0, 0]]]], [[3, 13, 5, 5, 1], [0 < v, (v^2+2)^(1/2) < u, And(1 < x,x < u^2-v^2-\
1), u^2-v^2-x-1 < y, z = z], [regular_chain, [[1, 1], [3, 3], [4, 4], [4, 4],
[0, 0]]]], [[1, 13, 2, 2, 1], [v < 0, (v^2+2)^(1/2) < u, x = -1, y = -u^2+v^2,
z = z], [regular_chain, [[-1, -1], [3, 3], [-1, -1], [-8, -8], [0, 0]]]], [[2,
4, 6, 4, 1], [v = 0, u = -1, x = 1, y = 1, z < 0], [regular_chain, [[0, 0], [-\
1, -1], [1, 1], [1, 1], [-1, -1]]]], [[2, 4, 6, 4, 2], [v = 0, u = -1, x = 1,
y = 1, z = 0], [regular_chain, [[0, 0], [-1, -1], [1, 1], [1, 1], [0, 0]]]], [
[2, 4, 6, 4, 3], [v = 0, u = -1, x = 1, y = 1, 0 < z], [regular_chain, [[0, 0]
, [-1, -1], [1, 1], [1, 1], [1, 1]]]], [[3, 3, 6, 1, 1], [0 < v, And(-(v^2+2)^
(1/2) < u,u < -(v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, z = z], [regular_chain, [
[1, 1], [-6598195/4194304, -6598195/4194304], [1, 1], [-2, -2], [0, 0]]]], [[3
, 8, 3, 3, 1], [0 < v, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z < -1
], [regular_chain, [[1, 1], [1, 1], [0, 0], [0, 0], [-2, -2]]]], [[3, 8, 3, 3,
2], [0 < v, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z = -1], [
regular_chain, [[1, 1], [1, 1], [0, 0], [0, 0], [-1, -1]]]], [[3, 8, 3, 3, 3],
[0 < v, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [1, 1], [0, 0], [0, 0], [0, 0]]]], [[3, 8, 3, 3, 4], [
0 < v, u = v, And(-1 < x,x < 1), And(-1-x < y,y < x+1), z = 1], [regular_chain
, [[1, 1], [1, 1], [0, 0], [0, 0], [1, 1]]]], [[3, 8, 3, 3, 5], [0 < v, u = v,
And(-1 < x,x < 1), And(-1-x < y,y < x+1), 1 < z], [regular_chain, [[1, 1], [1,
1], [0, 0], [0, 0], [2, 2]]]], [[1, 3, 5, 4, 1], [v < 0, And(-(v^2+2)^(1/2) <
u,u < -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [1546383/
2097152, 1546383/2097152], [275385/1048576, 137693/524288], [0, 0]]]], [[1, 8,
3, 1, 1], [v < 0, u = -v, And(-1 < x,x < 1), y < -1-x, z < -1], [regular_chain
, [[-1, -1], [1, 1], [0, 0], [-2, -2], [-2, -2]]]], [[1, 8, 3, 1, 2], [v < 0,
u = -v, And(-1 < x,x < 1), y < -1-x, z = -1], [regular_chain, [[-1, -1], [1, 1
], [0, 0], [-2, -2], [-1, -1]]]], [[1, 8, 3, 1, 3], [v < 0, u = -v, And(-1 < x
,x < 1), y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [0,
0], [-2, -2], [0, 0]]]], [[1, 8, 3, 1, 4], [v < 0, u = -v, And(-1 < x,x < 1),
y < -1-x, z = 1], [regular_chain, [[-1, -1], [1, 1], [0, 0], [-2, -2], [1, 1]]
]], [[1, 8, 3, 1, 5], [v < 0, u = -v, And(-1 < x,x < 1), y < -1-x, 1 < z], [
regular_chain, [[-1, -1], [1, 1], [0, 0], [-2, -2], [2, 2]]]], [[2, 5, 2, 3, 1
], [v = 0, And(-1 < u,u < 0), x = -1, And(-u^2 < y,y < u^2), z < -(-u^2+1)^(1/
2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [0, 0], [-2, -2]]]], [[2
, 5, 2, 3, 2], [v = 0, And(-1 < u,u < 0), x = -1, And(-u^2 < y,y < u^2), z = -
(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [0, 0], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 5, 2, 3, 3], [v = 0, And(-1 < u,u
< 0), x = -1, And(-u^2 < y,y < u^2), And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2
))], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [0, 0], [-1/8388608, -1/
8388608]]]], [[2, 5, 2, 3, 4], [v = 0, And(-1 < u,u < 0), x = -1, And(-u^2 < y
,y < u^2), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1
], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 5, 2, 3, 5], [v = 0, And(-\
1 < u,u < 0), x = -1, And(-u^2 < y,y < u^2), (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [0, 0], [2, 2]]]], [[2, 9, 6,
5, 1], [v = 0, And(1 < u,u < 2^(1/2)), x = 1, -u^2+2 < y, z = z], [
regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [1, 1], [2, 2], [0
, 0]]]], [[3, 13, 5, 4, 1], [0 < v, (v^2+2)^(1/2) < u, And(1 < x,x < u^2-v^2-1
), y = u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3, 3], [4, 4], [3, 3], [
0, 0]]]], [[1, 13, 2, 1, 1], [v < 0, (v^2+2)^(1/2) < u, x = -1, y < -u^2+v^2,
z = z], [regular_chain, [[-1, -1], [3, 3], [-1, -1], [-9, -9], [0, 0]]]], [[2,
4, 6, 3, 1], [v = 0, u = -1, x = 1, And(-1 < y,y < 1), z < 0], [regular_chain,
[[0, 0], [-1, -1], [1, 1], [0, 0], [-1, -1]]]], [[2, 4, 6, 3, 2], [v = 0, u =
-1, x = 1, And(-1 < y,y < 1), z = 0], [regular_chain, [[0, 0], [-1, -1], [1, 1
], [0, 0], [0, 0]]]], [[2, 4, 6, 3, 3], [v = 0, u = -1, x = 1, And(-1 < y,y <
1), 0 < z], [regular_chain, [[0, 0], [-1, -1], [1, 1], [0, 0], [1, 1]]]], [[3,
3, 6, 2, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = 1, y = u^
2-v^2-2, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304]
, [1, 1], [-275385/524288, -1101539/2097152], [0, 0]]]], [[3, 8, 3, 4, 1], [0
< v, u = v, And(-1 < x,x < 1), y = x+1, z < -1], [regular_chain, [[1, 1], [1,
1], [0, 0], [1, 1], [-2, -2]]]], [[3, 8, 3, 4, 2], [0 < v, u = v, And(-1 < x,x
< 1), y = x+1, z = -1], [regular_chain, [[1, 1], [1, 1], [0, 0], [1, 1], [-1,
-1]]]], [[3, 8, 3, 4, 3], [0 < v, u = v, And(-1 < x,x < 1), y = x+1, And(-1 <
z,z < 1)], [regular_chain, [[1, 1], [1, 1], [0, 0], [1, 1], [0, 0]]]], [[3, 8,
3, 4, 4], [0 < v, u = v, And(-1 < x,x < 1), y = x+1, z = 1], [regular_chain, [
[1, 1], [1, 1], [0, 0], [1, 1], [1, 1]]]], [[3, 8, 3, 4, 5], [0 < v, u = v, 
And(-1 < x,x < 1), y = x+1, 1 < z], [regular_chain, [[1, 1], [1, 1], [0, 0], [
1, 1], [2, 2]]]], [[1, 12, 5, 5, 1], [v < 0, u = (v^2+2)^(1/2), 1 < x, x-1 < y
, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [2, 2],
[2, 2], [0, 0]]]], [[2, 4, 6, 1, 1], [v = 0, u = -1, x = 1, y < -1, z < 0], [
regular_chain, [[0, 0], [-1, -1], [1, 1], [-2, -2], [-1, -1]]]], [[2, 4, 6, 1,
2], [v = 0, u = -1, x = 1, y < -1, z = 0], [regular_chain, [[0, 0], [-1, -1],
[1, 1], [-2, -2], [0, 0]]]], [[2, 4, 6, 1, 3], [v = 0, u = -1, x = 1, y < -1,
0 < z], [regular_chain, [[0, 0], [-1, -1], [1, 1], [-2, -2], [1, 1]]]], [[3, 4
, 1, 2, 1], [0 < v, u = -(v^2+1)^(1/2), x < -1, y = x, z < 0], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [-2, -2], [-1, -1]]]],
[[3, 4, 1, 2, 2], [0 < v, u = -(v^2+1)^(1/2), x < -1, y = x, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [-2, -2]
, [0, 0]]]], [[3, 4, 1, 2, 3], [0 < v, u = -(v^2+1)^(1/2), x < -1, y = x, 0 <
z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [-2
, -2], [1, 1]]]], [[3, 9, 1, 3, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x <
-1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [0, 0],
[-2, -2]]]], [[3, 9, 1, 3, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, 
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [0, 0], [-772605/
1048576, -1545209/2097152]]]], [[3, 9, 1, 3, 3], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 
1265743/1048576], [-2, -2], [0, 0], [-1/4194304, -1/4194304]]]], [[3, 9, 1, 3,
4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, And(x-u^2+v^2+1 < y,y < u^2-
v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576,
1265743/1048576], [-2, -2], [0, 0], [193151/262144, 772605/1048576]]]], [[3, 9
, 1, 3, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, And(x-u^2+v^2+1 < y,
y < u^2-v^2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-2, -2], [0, 0], [2, 2]]]], [[1, 3, 2, 3, 1], [v <
0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u^
2-v^2), z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304
], [-1, -1], [0, 0], [0, 0]]]], [[1, 7, 7, 4, 1], [v < 0, And(v < u,u < -v), 1
< x, y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0,
0], [2, 2], [4, 4], [-3, -3]]]], [[1, 7, 7, 4, 2], [v < 0, And(v < u,u < -v),
1 < x, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
0, 0], [2, 2], [4, 4], [-1482911/1048576, -741455/524288]]]], [[1, 7, 7, 4, 3]
, [v < 0, And(v < u,u < -v), 1 < x, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) <
z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [2, 2], [4, 4],
[0, 0]]]], [[1, 7, 7, 4, 4], [v < 0, And(v < u,u < -v), 1 < x, y = x-u^2+v^2+1
, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [2, 2], [4, 4],
[741455/524288, 1482911/1048576]]]], [[1, 7, 7, 4, 5], [v < 0, And(v < u,u < -
v), 1 < x, y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1]
, [0, 0], [2, 2], [4, 4], [3, 3]]]], [[2, 5, 2, 5, 1], [v = 0, And(-1 < u,u <
0), x = -1, u^2 < y, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/
2], [-1, -1], [2, 2], [-2, -2]]]], [[2, 5, 2, 5, 2], [v = 0, And(-1 < u,u < 0)
, x = -1, u^2 < y, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2]
, [-1, -1], [2, 2], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 2, 5, 3],
[v = 0, And(-1 < u,u < 0), x = -1, u^2 < y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+
1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [2, 2], [-1/
8388608, -1/8388608]]]], [[2, 5, 2, 5, 4], [v = 0, And(-1 < u,u < 0), x = -1,
u^2 < y, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1],
[2, 2], [908093/1048576, 454047/524288]]]], [[2, 5, 2, 5, 5], [v = 0, And(-1 <
u,u < 0), x = -1, u^2 < y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2
, -1/2], [-1, -1], [2, 2], [2, 2]]]], [[2, 10, 1, 1, 1], [v = 0, u = 2^(1/2),
x < -1, y < x-1, z = z], [regular_chain, [[0, 0], [741455/524288, 1482911/
1048576], [-2, -2], [-4, -4], [0, 0]]]], [[3, 13, 2, 5, 1], [0 < v, (v^2+2)^(1
/2) < u, x = -1, u^2-v^2 < y, z = z], [regular_chain, [[1, 1], [3, 3], [-1, -1
], [9, 9], [0, 0]]]], [[1, 13, 1, 1, 1], [v < 0, (v^2+2)^(1/2) < u, x < -1, y
< x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [3, 3], [-2, -2], [-10, -10]
, [0, 0]]]], [[2, 4, 6, 2, 1], [v = 0, u = -1, x = 1, y = -1, z < 0], [
regular_chain, [[0, 0], [-1, -1], [1, 1], [-1, -1], [-1, -1]]]], [[2, 4, 6, 2,
2], [v = 0, u = -1, x = 1, y = -1, z = 0], [regular_chain, [[0, 0], [-1, -1],
[1, 1], [-1, -1], [0, 0]]]], [[2, 4, 6, 2, 3], [v = 0, u = -1, x = 1, y = -1,
0 < z], [regular_chain, [[0, 0], [-1, -1], [1, 1], [-1, -1], [1, 1]]]], [[3, 4
, 1, 1, 1], [0 < v, u = -(v^2+1)^(1/2), x < -1, y < x, z < 0], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [-3, -3], [-1, -1]]]],
[[3, 4, 1, 1, 2], [0 < v, u = -(v^2+1)^(1/2), x < -1, y < x, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [-3, -3]
, [0, 0]]]], [[3, 4, 1, 1, 3], [0 < v, u = -(v^2+1)^(1/2), x < -1, y < x, 0 <
z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [-3
, -3], [1, 1]]]], [[3, 9, 1, 2, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x <
-1, y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
1265743/1048576, 1265743/1048576], [-2, -2], [-1527887/1048576, -763943/524288
], [-2, -2]]]], [[3, 9, 1, 2, 2], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1
, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743
/1048576, 1265743/1048576], [-2, -2], [-1527887/1048576, -763943/524288], [-\
772605/1048576, -1545209/2097152]]]], [[3, 9, 1, 2, 3], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2
+v^2+1)^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576],
[-2, -2], [-1527887/1048576, -763943/524288], [-1/4194304, -1/4194304]]]], [[3
, 9, 1, 2, 4], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/
1048576], [-2, -2], [-1527887/1048576, -763943/524288], [193151/262144, 772605
/1048576]]]], [[3, 9, 1, 2, 5], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1,
y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [1265743/
1048576, 1265743/1048576], [-2, -2], [-1527887/1048576, -763943/524288], [2, 2
]]]], [[1, 3, 2, 4, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x
= -1, y = u^2-v^2, z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -\
6598195/4194304], [-1, -1], [773191/524288, 1546383/1048576], [0, 0]]]], [[1,
7, 7, 5, 1], [v < 0, And(v < u,u < -v), 1 < x, x-u^2+v^2+1 < y, z < -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [2, 2], [5, 5], [-3, -3]]]], [[
1, 7, 7, 5, 2], [v < 0, And(v < u,u < -v), 1 < x, x-u^2+v^2+1 < y, z = -(-u^2+
v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [2, 2], [5, 5], [-1482911/
1048576, -741455/524288]]]], [[1, 7, 7, 5, 3], [v < 0, And(v < u,u < -v), 1 <
x, x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [2, 2], [5, 5], [0, 0]]]], [[1, 7, 7, 5, 4],
[v < 0, And(v < u,u < -v), 1 < x, x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [2, 2], [5, 5], [741455/524288, 1482911/
1048576]]]], [[1, 7, 7, 5, 5], [v < 0, And(v < u,u < -v), 1 < x, x-u^2+v^2+1 <
y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [2, 2], [5, 5],
[3, 3]]]], [[2, 5, 2, 4, 1], [v = 0, And(-1 < u,u < 0), x = -1, y = u^2, z < -
(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [1/4, 1/4],
[-2, -2]]]], [[2, 5, 2, 4, 2], [v = 0, And(-1 < u,u < 0), x = -1, y = u^2, z =
-(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [1/4, 1/4],
[-1816187/2097152, -3632373/4194304]]]], [[2, 5, 2, 4, 3], [v = 0, And(-1 < u,
u < 0), x = -1, y = u^2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [1/4, 1/4], [-1/8388608, -1/
8388608]]]], [[2, 5, 2, 4, 4], [v = 0, And(-1 < u,u < 0), x = -1, y = u^2, z =
(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-1, -1], [1/4, 1/4],
[908093/1048576, 454047/524288]]]], [[2, 5, 2, 4, 5], [v = 0, And(-1 < u,u < 0
), x = -1, y = u^2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2]
, [-1, -1], [1/4, 1/4], [2, 2]]]], [[2, 9, 7, 5, 1], [v = 0, And(1 < u,u < 2^(
1/2)), 1 < x, x-u^2+1 < y, z = z], [regular_chain, [[0, 0], [1265743/1048576,
1265743/1048576], [2, 2], [3, 3], [0, 0]]]], [[3, 13, 3, 1, 1], [0 < v, (v^2+2
)^(1/2) < u, And(-1 < x,x < 1), y < x-u^2+v^2+1, z = z], [regular_chain, [[1,
1], [3, 3], [0, 0], [-8, -8], [0, 0]]]], [[1, 13, 1, 2, 1], [v < 0, (v^2+2)^(1
/2) < u, x < -1, y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [3, 3], [
-2, -2], [-9, -9], [0, 0]]]], [[2, 4, 5, 4, 1], [v = 0, u = -1, And(0 < x,x <
1), y = x, z < 0], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [1/2, 1/2],
[-1, -1]]]], [[2, 4, 5, 4, 2], [v = 0, u = -1, And(0 < x,x < 1), y = x, z = 0]
, [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [1/2, 1/2], [0, 0]]]], [[2, 4
, 5, 4, 3], [v = 0, u = -1, And(0 < x,x < 1), y = x, 0 < z], [regular_chain, [
[0, 0], [-1, -1], [1/2, 1/2], [1/2, 1/2], [1, 1]]]], [[3, 4, 1, 4, 1], [0 < v,
u = -(v^2+1)^(1/2), x < -1, y = -x, z < 0], [regular_chain, [[1, 1], [-1482911
/1048576, -741455/524288], [-2, -2], [2, 2], [-1, -1]]]], [[3, 4, 1, 4, 2], [0
< v, u = -(v^2+1)^(1/2), x < -1, y = -x, z = 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [-2, -2], [2, 2], [0, 0]]]], [[3, 4, 1, 4, 3
], [0 < v, u = -(v^2+1)^(1/2), x < -1, y = -x, 0 < z], [regular_chain, [[1, 1]
, [-1482911/1048576, -741455/524288], [-2, -2], [2, 2], [1, 1]]]], [[3, 9, 1,
1, 1], [0 < v, And(v < u,u < (v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, z < -(-u
^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576],
[-2, -2], [-3, -3], [-2, -2]]]], [[3, 9, 1, 1, 2], [0 < v, And(v < u,u < (v^2+
1)^(1/2)), x < -1, y < x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [-3, -3], [-772605/
1048576, -1545209/2097152]]]], [[3, 9, 1, 1, 3], [0 < v, And(v < u,u < (v^2+1)
^(1/2)), x < -1, y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)
^(1/2))], [regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2
], [-3, -3], [-1/4194304, -1/4194304]]]], [[3, 9, 1, 1, 4], [0 < v, And(v < u,
u < (v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [-3, -3]
, [193151/262144, 772605/1048576]]]], [[3, 9, 1, 1, 5], [0 < v, And(v < u,u <
(v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [1265743/1048576, 1265743/1048576], [-2, -2], [-3, -3]
, [2, 2]]]], [[1, 3, 2, 5, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/
2)), x = -1, u^2-v^2 < y, z = z], [regular_chain, [[-1, -1], [-6598195/4194304
, -6598195/4194304], [-1, -1], [3, 3], [0, 0]]]], [[1, 7, 7, 2, 1], [v < 0, 
And(v < u,u < -v), 1 < x, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [2, 2], [-4, -4], [-3, -3]]]], [[1, 7, 7, 2,
2], [v < 0, And(v < u,u < -v), 1 < x, y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)
], [regular_chain, [[-1, -1], [0, 0], [2, 2], [-4, -4], [-1482911/1048576, -\
741455/524288]]]], [[1, 7, 7, 2, 3], [v < 0, And(v < u,u < -v), 1 < x, y = u^2
-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain
, [[-1, -1], [0, 0], [2, 2], [-4, -4], [0, 0]]]], [[1, 7, 7, 2, 4], [v < 0, 
And(v < u,u < -v), 1 < x, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [2, 2], [-4, -4], [741455/524288, 1482911/
1048576]]]], [[1, 7, 7, 2, 5], [v < 0, And(v < u,u < -v), 1 < x, y = u^2-v^2-x
-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [2, 2], [-4, -\
4], [3, 3]]]], [[2, 5, 3, 2, 1], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2
-1), y = x-u^2+1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2],
[-7/8, -7/8], [-1/8, -1/8], [-2, -2]]]], [[2, 5, 3, 2, 2], [v = 0, And(-1 < u,
u < 0), And(-1 < x,x < u^2-1), y = x-u^2+1, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [-1/8, -1/8], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 3, 2, 3], [v = 0, And(-1 < u,u < 0), 
And(-1 < x,x < u^2-1), y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2)
)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [-1/8, -1/8], [-1/
8388608, -1/8388608]]]], [[2, 5, 3, 2, 4], [v = 0, And(-1 < u,u < 0), And(-1 <
x,x < u^2-1), y = x-u^2+1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2
, -1/2], [-7/8, -7/8], [-1/8, -1/8], [908093/1048576, 454047/524288]]]], [[2,
5, 3, 2, 5], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y = x-u^2+1, (-
u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [-1/8,
-1/8], [2, 2]]]], [[2, 9, 7, 4, 1], [v = 0, And(1 < u,u < 2^(1/2)), 1 < x, y =
x-u^2+1, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576],
[2, 2], [1617841/1048576, 808921/524288], [0, 0]]]], [[3, 13, 3, 2, 1], [0 < v
, (v^2+2)^(1/2) < u, And(-1 < x,x < 1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [3, 3], [0, 0], [-7, -7], [0, 0]]]], [[1, 13, 1, 3, 1]
, [v < 0, (v^2+2)^(1/2) < u, x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z =
z], [regular_chain, [[-1, -1], [3, 3], [-2, -2], [0, 0], [0, 0]]]], [[2, 4, 5,
5, 1], [v = 0, u = -1, And(0 < x,x < 1), x < y, z < 0], [regular_chain, [[0, 0
], [-1, -1], [1/2, 1/2], [2, 2], [-1, -1]]]], [[2, 4, 5, 5, 2], [v = 0, u = -1
, And(0 < x,x < 1), x < y, z = 0], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/
2], [2, 2], [0, 0]]]], [[2, 4, 5, 5, 3], [v = 0, u = -1, And(0 < x,x < 1), x <
y, 0 < z], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [2, 2], [1, 1]]]], [
[3, 4, 1, 3, 1], [0 < v, u = -(v^2+1)^(1/2), x < -1, And(x < y,y < -x), z < 0]
, [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-2, -2], [0, 0
], [-1, -1]]]], [[3, 4, 1, 3, 2], [0 < v, u = -(v^2+1)^(1/2), x < -1, And(x <
y,y < -x), z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288]
, [-2, -2], [0, 0], [0, 0]]]], [[3, 4, 1, 3, 3], [0 < v, u = -(v^2+1)^(1/2), x
< -1, And(x < y,y < -x), 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [-2, -2], [0, 0], [1, 1]]]], [[3, 8, 5, 5, 1], [0 < v, u = v,
1 < x, x+1 < y, z < -1], [regular_chain, [[1, 1], [1, 1], [2, 2], [4, 4], [-2,
-2]]]], [[3, 8, 5, 5, 2], [0 < v, u = v, 1 < x, x+1 < y, z = -1], [
regular_chain, [[1, 1], [1, 1], [2, 2], [4, 4], [-1, -1]]]], [[3, 8, 5, 5, 3],
[0 < v, u = v, 1 < x, x+1 < y, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1
, 1], [2, 2], [4, 4], [0, 0]]]], [[3, 8, 5, 5, 4], [0 < v, u = v, 1 < x, x+1 <
y, z = 1], [regular_chain, [[1, 1], [1, 1], [2, 2], [4, 4], [1, 1]]]], [[3, 8,
5, 5, 5], [0 < v, u = v, 1 < x, x+1 < y, 1 < z], [regular_chain, [[1, 1], [1,
1], [2, 2], [4, 4], [2, 2]]]], [[1, 3, 3, 1, 1], [v < 0, And(-(v^2+2)^(1/2) <
u,u < -(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-275385/
1048576, -275385/1048576], [-2, -2], [0, 0]]]], [[1, 7, 7, 3, 1], [v < 0, And(
v < u,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^
(1/2)], [regular_chain, [[-1, -1], [0, 0], [2, 2], [0, 0], [-3, -3]]]], [[1, 7
, 7, 3, 2], [v < 0, And(v < u,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^
2+1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [2, 2], [0,
0], [-1482911/1048576, -741455/524288]]]], [[1, 7, 7, 3, 3], [v < 0, And(v < u
,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [2, 2], [0, 0
], [0, 0]]]], [[1, 7, 7, 3, 4], [v < 0, And(v < u,u < -v), 1 < x, And(u^2-v^2-
x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1],
[0, 0], [2, 2], [0, 0], [741455/524288, 1482911/1048576]]]], [[1, 7, 7, 3, 5],
[v < 0, And(v < u,u < -v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+
v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [2, 2], [0, 0], [3, 3]]]
], [[2, 5, 3, 1, 1], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y < x-u
^2+1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8
], [-2, -2], [-2, -2]]]], [[2, 5, 3, 1, 2], [v = 0, And(-1 < u,u < 0), And(-1
< x,x < u^2-1), y < x-u^2+1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-\
1/2, -1/2], [-7/8, -7/8], [-2, -2], [-1816187/2097152, -3632373/4194304]]]], [
[2, 5, 3, 1, 3], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y < x-u^2+1
, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2
, -1/2], [-7/8, -7/8], [-2, -2], [-1/8388608, -1/8388608]]]], [[2, 5, 3, 1, 4]
, [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y < x-u^2+1, z = (-u^2+1)^
(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [-2, -2], [908093
/1048576, 454047/524288]]]], [[2, 5, 3, 1, 5], [v = 0, And(-1 < u,u < 0), And(
-1 < x,x < u^2-1), y < x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0],
[-1/2, -1/2], [-7/8, -7/8], [-2, -2], [2, 2]]]], [[2, 9, 7, 3, 1], [v = 0, And
(1 < u,u < 2^(1/2)), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), z = z], [
regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [2, 2], [0, 0], [0
, 0]]]], [[3, 13, 3, 3, 1], [0 < v, (v^2+2)^(1/2) < u, And(-1 < x,x < 1), And(
x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[1, 1], [3, 3], [0,
0], [0, 0], [0, 0]]]], [[1, 3, 3, 2, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(
v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [-275385/
1048576, -275385/1048576], [-1546383/2097152, -773191/1048576], [0, 0]]]], [[1
, 8, 1, 3, 1], [v < 0, u = -v, x < -1, And(x+1 < y,y < -1-x), z < -1], [
regular_chain, [[-1, -1], [1, 1], [-2, -2], [0, 0], [-2, -2]]]], [[1, 8, 1, 3,
2], [v < 0, u = -v, x < -1, And(x+1 < y,y < -1-x), z = -1], [regular_chain, [[
-1, -1], [1, 1], [-2, -2], [0, 0], [-1, -1]]]], [[1, 8, 1, 3, 3], [v < 0, u =
-v, x < -1, And(x+1 < y,y < -1-x), And(-1 < z,z < 1)], [regular_chain, [[-1, -\
1], [1, 1], [-2, -2], [0, 0], [0, 0]]]], [[1, 8, 1, 3, 4], [v < 0, u = -v, x <
-1, And(x+1 < y,y < -1-x), z = 1], [regular_chain, [[-1, -1], [1, 1], [-2, -2]
, [0, 0], [1, 1]]]], [[1, 8, 1, 3, 5], [v < 0, u = -v, x < -1, And(x+1 < y,y <
-1-x), 1 < z], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [0, 0], [2, 2]]]],
[[2, 5, 3, 4, 1], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y = u^2-x-\
1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8],
[1/8, 1/8], [-2, -2]]]], [[2, 5, 3, 4, 2], [v = 0, And(-1 < u,u < 0), And(-1 <
x,x < u^2-1), y = u^2-x-1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/
2, -1/2], [-7/8, -7/8], [1/8, 1/8], [-1816187/2097152, -3632373/4194304]]]], [
[2, 5, 3, 4, 3], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y = u^2-x-1
, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2
, -1/2], [-7/8, -7/8], [1/8, 1/8], [-1/8388608, -1/8388608]]]], [[2, 5, 3, 4,
4], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), y = u^2-x-1, z = (-u^2+1
)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [1/8, 1/8], [
908093/1048576, 454047/524288]]]], [[2, 5, 3, 4, 5], [v = 0, And(-1 < u,u < 0)
, And(-1 < x,x < u^2-1), y = u^2-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [[0
, 0], [-1/2, -1/2], [-7/8, -7/8], [1/8, 1/8], [2, 2]]]], [[2, 10, 1, 5, 1], [v
= 0, u = 2^(1/2), x < -1, 1-x < y, z = z], [regular_chain, [[0, 0], [741455/
524288, 1482911/1048576], [-2, -2], [4, 4], [0, 0]]]], [[3, 13, 3, 4, 1], [0 <
v, (v^2+2)^(1/2) < u, And(-1 < x,x < 1), y = u^2-v^2-x-1, z = z], [
regular_chain, [[1, 1], [3, 3], [0, 0], [7, 7], [0, 0]]]], [[1, 12, 5, 1, 1],
[v < 0, u = (v^2+2)^(1/2), 1 < x, y < 1-x, z = z], [regular_chain, [[-1, -1],
[908093/524288, 1816187/1048576], [2, 2], [-2, -2], [0, 0]]]], [[2, 4, 5, 2, 1
], [v = 0, u = -1, And(0 < x,x < 1), y = -x, z < 0], [regular_chain, [[0, 0],
[-1, -1], [1/2, 1/2], [-1/2, -1/2], [-1, -1]]]], [[2, 4, 5, 2, 2], [v = 0, u =
-1, And(0 < x,x < 1), y = -x, z = 0], [regular_chain, [[0, 0], [-1, -1], [1/2,
1/2], [-1/2, -1/2], [0, 0]]]], [[2, 4, 5, 2, 3], [v = 0, u = -1, And(0 < x,x <
1), y = -x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [-1/2, -1/2
], [1, 1]]]], [[3, 3, 7, 3, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1
/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [regular_chain, [[1
, 1], [-6598195/4194304, -6598195/4194304], [2, 2], [-1/4194304, -1/4194304],
[0, 0]]]], [[3, 8, 5, 4, 1], [0 < v, u = v, 1 < x, y = x+1, z < -1], [
regular_chain, [[1, 1], [1, 1], [2, 2], [3, 3], [-2, -2]]]], [[3, 8, 5, 4, 2],
[0 < v, u = v, 1 < x, y = x+1, z = -1], [regular_chain, [[1, 1], [1, 1], [2, 2
], [3, 3], [-1, -1]]]], [[3, 8, 5, 4, 3], [0 < v, u = v, 1 < x, y = x+1, And(-\
1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [2, 2], [3, 3], [0, 0]]]], [[3
, 8, 5, 4, 4], [0 < v, u = v, 1 < x, y = x+1, z = 1], [regular_chain, [[1, 1],
[1, 1], [2, 2], [3, 3], [1, 1]]]], [[3, 8, 5, 4, 5], [0 < v, u = v, 1 < x, y =
x+1, 1 < z], [regular_chain, [[1, 1], [1, 1], [2, 2], [3, 3], [2, 2]]]], [[1,
3, 3, 3, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(-1 < x,x
< u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [regular_chain, [[
-1, -1], [-6598195/4194304, -6598195/4194304], [-275385/1048576, -275385/
1048576], [0, 0], [0, 0]]]], [[1, 8, 1, 4, 1], [v < 0, u = -v, x < -1, y = -1-
x, z < -1], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [1, 1], [-2, -2]]]],
[[1, 8, 1, 4, 2], [v < 0, u = -v, x < -1, y = -1-x, z = -1], [regular_chain, [
[-1, -1], [1, 1], [-2, -2], [1, 1], [-1, -1]]]], [[1, 8, 1, 4, 3], [v < 0, u =
-v, x < -1, y = -1-x, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [
-2, -2], [1, 1], [0, 0]]]], [[1, 8, 1, 4, 4], [v < 0, u = -v, x < -1, y = -1-x
, z = 1], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [1, 1], [1, 1]]]], [[1,
8, 1, 4, 5], [v < 0, u = -v, x < -1, y = -1-x, 1 < z], [regular_chain, [[-1, -\
1], [1, 1], [-2, -2], [1, 1], [2, 2]]]], [[2, 5, 3, 3, 1], [v = 0, And(-1 < u,
u < 0), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), z < -(-u^2+1)^(1/
2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [0, 0], [-2, -2]]]],
[[2, 5, 3, 3, 2], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), And(x-u^2+
1 < y,y < u^2-x-1), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2
], [-7/8, -7/8], [0, 0], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 3, 3
, 3], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^
2-x-1), And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0],
[-1/2, -1/2], [-7/8, -7/8], [0, 0], [-1/8388608, -1/8388608]]]], [[2, 5, 3, 3,
4], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-
x-1), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8]
, [0, 0], [908093/1048576, 454047/524288]]]], [[2, 5, 3, 3, 5], [v = 0, And(-1
< u,u < 0), And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), (-u^2+1)^(1/2
) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [0, 0], [2, 2]]]]
, [[2, 10, 1, 4, 1], [v = 0, u = 2^(1/2), x < -1, y = 1-x, z = z], [
regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [-2, -2], [3, 3], [0
, 0]]]], [[3, 13, 3, 5, 1], [0 < v, (v^2+2)^(1/2) < u, And(-1 < x,x < 1), u^2-
v^2-x-1 < y, z = z], [regular_chain, [[1, 1], [3, 3], [0, 0], [8, 8], [0, 0]]]
], [[1, 12, 5, 2, 1], [v < 0, u = (v^2+2)^(1/2), 1 < x, y = 1-x, z = z], [
regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [2, 2], [-1, -1],
[0, 0]]]], [[2, 4, 5, 3, 1], [v = 0, u = -1, And(0 < x,x < 1), And(-x < y,y <
x), z < 0], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [0, 0], [-1, -1]]]]
, [[2, 4, 5, 3, 2], [v = 0, u = -1, And(0 < x,x < 1), And(-x < y,y < x), z = 0
], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [0, 0], [0, 0]]]], [[2, 4, 5
, 3, 3], [v = 0, u = -1, And(0 < x,x < 1), And(-x < y,y < x), 0 < z], [
regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [0, 0], [1, 1]]]], [[3, 3, 7, 2,
1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1
, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [2, 2
], [-799673/524288, -3198691/2097152], [0, 0]]]], [[3, 8, 5, 3, 1], [0 < v, u
= v, 1 < x, And(-1-x < y,y < x+1), z < -1], [regular_chain, [[1, 1], [1, 1], [
2, 2], [0, 0], [-2, -2]]]], [[3, 8, 5, 3, 2], [0 < v, u = v, 1 < x, And(-1-x <
y,y < x+1), z = -1], [regular_chain, [[1, 1], [1, 1], [2, 2], [0, 0], [-1, -1]
]]], [[3, 8, 5, 3, 3], [0 < v, u = v, 1 < x, And(-1-x < y,y < x+1), And(-1 < z
,z < 1)], [regular_chain, [[1, 1], [1, 1], [2, 2], [0, 0], [0, 0]]]], [[3, 8,
5, 3, 4], [0 < v, u = v, 1 < x, And(-1-x < y,y < x+1), z = 1], [regular_chain,
[[1, 1], [1, 1], [2, 2], [0, 0], [1, 1]]]], [[3, 8, 5, 3, 5], [0 < v, u = v, 1
< x, And(-1-x < y,y < x+1), 1 < z], [regular_chain, [[1, 1], [1, 1], [2, 2], [
0, 0], [2, 2]]]], [[1, 3, 3, 4, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1
)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = z], [regular_chain,
[[-1, -1], [-6598195/4194304, -6598195/4194304], [-275385/1048576, -275385/
1048576], [773191/1048576, 96649/131072], [0, 0]]]], [[1, 8, 1, 1, 1], [v < 0,
u = -v, x < -1, y < x+1, z < -1], [regular_chain, [[-1, -1], [1, 1], [-2, -2],
[-2, -2], [-2, -2]]]], [[1, 8, 1, 1, 2], [v < 0, u = -v, x < -1, y < x+1, z =
-1], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [-2, -2], [-1, -1]]]], [[1,
8, 1, 1, 3], [v < 0, u = -v, x < -1, y < x+1, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [1, 1], [-2, -2], [-2, -2], [0, 0]]]], [[1, 8, 1, 1,
4], [v < 0, u = -v, x < -1, y < x+1, z = 1], [regular_chain, [[-1, -1], [1, 1]
, [-2, -2], [-2, -2], [1, 1]]]], [[1, 8, 1, 1, 5], [v < 0, u = -v, x < -1, y <
x+1, 1 < z], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [-2, -2], [2, 2]]]],
[[2, 5, 4, 1, 1], [v = 0, And(-1 < u,u < 0), x = u^2-1, y < 0, z < -(-u^2+1)^(
1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [-1, -1], [-2, -2]
]]], [[2, 5, 4, 1, 2], [v = 0, And(-1 < u,u < 0), x = u^2-1, y < 0, z = -(-u^2
+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [-1, -1], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 5, 4, 1, 3], [v = 0, And(-1 < u,u
< 0), x = u^2-1, y < 0, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [-1, -1], [-1/8388608, -1/
8388608]]]], [[2, 5, 4, 1, 4], [v = 0, And(-1 < u,u < 0), x = u^2-1, y < 0, z
= (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [-1, -\
1], [908093/1048576, 454047/524288]]]], [[2, 5, 4, 1, 5], [v = 0, And(-1 < u,u
< 0), x = u^2-1, y < 0, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -\
1/2], [-3/4, -3/4], [-1, -1], [2, 2]]]], [[2, 10, 1, 3, 1], [v = 0, u = 2^(1/2
), x < -1, And(x-1 < y,y < 1-x), z = z], [regular_chain, [[0, 0], [741455/
524288, 1482911/1048576], [-2, -2], [0, 0], [0, 0]]]], [[3, 13, 4, 1, 1], [0 <
v, (v^2+2)^(1/2) < u, x = 1, y < -u^2+v^2+2, z = z], [regular_chain, [[1, 1],
[3, 3], [1, 1], [-7, -7], [0, 0]]]], [[1, 12, 5, 3, 1], [v < 0, u = (v^2+2)^(1
/2), 1 < x, And(1-x < y,y < x-1), z = z], [regular_chain, [[-1, -1], [908093/
524288, 1816187/1048576], [2, 2], [0, 0], [0, 0]]]], [[2, 4, 4, 3, 1], [v = 0,
u = -1, x = 0, 0 < y, z < 0], [regular_chain, [[0, 0], [-1, -1], [0, 0], [1, 1
], [-1, -1]]]], [[2, 4, 4, 3, 2], [v = 0, u = -1, x = 0, 0 < y, z = 0], [
regular_chain, [[0, 0], [-1, -1], [0, 0], [1, 1], [0, 0]]]], [[2, 4, 4, 3, 3],
[v = 0, u = -1, x = 0, 0 < y, 0 < z], [regular_chain, [[0, 0], [-1, -1], [0, 0
], [1, 1], [1, 1]]]], [[3, 3, 7, 5, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v
^2+1)^(1/2)), 1 < x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[1, 1], [-\
6598195/4194304, -6598195/4194304], [2, 2], [3, 3], [0, 0]]]], [[3, 8, 5, 2, 1
], [0 < v, u = v, 1 < x, y = -1-x, z < -1], [regular_chain, [[1, 1], [1, 1], [
2, 2], [-3, -3], [-2, -2]]]], [[3, 8, 5, 2, 2], [0 < v, u = v, 1 < x, y = -1-x
, z = -1], [regular_chain, [[1, 1], [1, 1], [2, 2], [-3, -3], [-1, -1]]]], [[3
, 8, 5, 2, 3], [0 < v, u = v, 1 < x, y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [1, 1], [2, 2], [-3, -3], [0, 0]]]], [[3, 8, 5, 2, 4],
[0 < v, u = v, 1 < x, y = -1-x, z = 1], [regular_chain, [[1, 1], [1, 1], [2, 2
], [-3, -3], [1, 1]]]], [[3, 8, 5, 2, 5], [0 < v, u = v, 1 < x, y = -1-x, 1 <
z], [regular_chain, [[1, 1], [1, 1], [2, 2], [-3, -3], [2, 2]]]], [[1, 3, 3, 5
, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(-1 < x,x < u^2-v
^2-1), u^2-v^2-x-1 < y, z = z], [regular_chain, [[-1, -1], [-6598195/4194304,
-6598195/4194304], [-275385/1048576, -275385/1048576], [2, 2], [0, 0]]]], [[1,
8, 1, 2, 1], [v < 0, u = -v, x < -1, y = x+1, z < -1], [regular_chain, [[-1, -\
1], [1, 1], [-2, -2], [-1, -1], [-2, -2]]]], [[1, 8, 1, 2, 2], [v < 0, u = -v,
x < -1, y = x+1, z = -1], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [-1, -1
], [-1, -1]]]], [[1, 8, 1, 2, 3], [v < 0, u = -v, x < -1, y = x+1, And(-1 < z,
z < 1)], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [-1, -1], [0, 0]]]], [[1
, 8, 1, 2, 4], [v < 0, u = -v, x < -1, y = x+1, z = 1], [regular_chain, [[-1,
-1], [1, 1], [-2, -2], [-1, -1], [1, 1]]]], [[1, 8, 1, 2, 5], [v < 0, u = -v,
x < -1, y = x+1, 1 < z], [regular_chain, [[-1, -1], [1, 1], [-2, -2], [-1, -1]
, [2, 2]]]], [[2, 5, 3, 5, 1], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1
), u^2-x-1 < y, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [
-7/8, -7/8], [2, 2], [-2, -2]]]], [[2, 5, 3, 5, 2], [v = 0, And(-1 < u,u < 0),
And(-1 < x,x < u^2-1), u^2-x-1 < y, z = -(-u^2+1)^(1/2)], [regular_chain, [[0,
0], [-1/2, -1/2], [-7/8, -7/8], [2, 2], [-1816187/2097152, -3632373/4194304]]]
], [[2, 5, 3, 5, 3], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), u^2-x-1
< y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-\
1/2, -1/2], [-7/8, -7/8], [2, 2], [-1/8388608, -1/8388608]]]], [[2, 5, 3, 5, 4
], [v = 0, And(-1 < u,u < 0), And(-1 < x,x < u^2-1), u^2-x-1 < y, z = (-u^2+1)
^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-7/8, -7/8], [2, 2], [908093/
1048576, 454047/524288]]]], [[2, 5, 3, 5, 5], [v = 0, And(-1 < u,u < 0), And(-\
1 < x,x < u^2-1), u^2-x-1 < y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [
-1/2, -1/2], [-7/8, -7/8], [2, 2], [2, 2]]]], [[2, 10, 1, 2, 1], [v = 0, u = 2
^(1/2), x < -1, y = x-1, z = z], [regular_chain, [[0, 0], [741455/524288, 
1482911/1048576], [-2, -2], [-3, -3], [0, 0]]]], [[3, 13, 4, 2, 1], [0 < v, (v
^2+2)^(1/2) < u, x = 1, y = -u^2+v^2+2, z = z], [regular_chain, [[1, 1], [3, 3
], [1, 1], [-6, -6], [0, 0]]]], [[1, 12, 5, 4, 1], [v < 0, u = (v^2+2)^(1/2),
1 < x, y = x-1, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/
1048576], [2, 2], [1, 1], [0, 0]]]], [[2, 4, 5, 1, 1], [v = 0, u = -1, And(0 <
x,x < 1), y < -x, z < 0], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [-2,
-2], [-1, -1]]]], [[2, 4, 5, 1, 2], [v = 0, u = -1, And(0 < x,x < 1), y < -x,
z = 0], [regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [-2, -2], [0, 0]]]], [[
2, 4, 5, 1, 3], [v = 0, u = -1, And(0 < x,x < 1), y < -x, 0 < z], [
regular_chain, [[0, 0], [-1, -1], [1/2, 1/2], [-2, -2], [1, 1]]]], [[3, 3, 7,
4, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), 1 < x, y = x-u^2+v^
2+1, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [2
, 2], [1599345/1048576, 799673/524288], [0, 0]]]], [[3, 8, 5, 1, 1], [0 < v, u
= v, 1 < x, y < -1-x, z < -1], [regular_chain, [[1, 1], [1, 1], [2, 2], [-4, -\
4], [-2, -2]]]], [[3, 8, 5, 1, 2], [0 < v, u = v, 1 < x, y < -1-x, z = -1], [
regular_chain, [[1, 1], [1, 1], [2, 2], [-4, -4], [-1, -1]]]], [[3, 8, 5, 1, 3
], [0 < v, u = v, 1 < x, y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[1, 1]
, [1, 1], [2, 2], [-4, -4], [0, 0]]]], [[3, 8, 5, 1, 4], [0 < v, u = v, 1 < x,
y < -1-x, z = 1], [regular_chain, [[1, 1], [1, 1], [2, 2], [-4, -4], [1, 1]]]]
, [[3, 8, 5, 1, 5], [0 < v, u = v, 1 < x, y < -1-x, 1 < z], [regular_chain, [[
1, 1], [1, 1], [2, 2], [-4, -4], [2, 2]]]], [[1, 13, 6, 2, 1], [v < 0, (v^2+2)
^(1/2) < u, x = u^2-v^2-1, y = 0, z = z], [regular_chain, [[-1, -1], [3, 3], [
7, 7], [0, 0], [0, 0]]]], [[2, 4, 3, 5, 1], [v = 0, u = -1, And(-1 < x,x < 0),
-x < y, z < 0], [regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [2, 2], [-1,
-1]]]], [[2, 4, 3, 5, 2], [v = 0, u = -1, And(-1 < x,x < 0), -x < y, z = 0], [
regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [2, 2], [0, 0]]]], [[2, 4, 3,
5, 3], [v = 0, u = -1, And(-1 < x,x < 0), -x < y, 0 < z], [regular_chain, [[0,
0], [-1, -1], [-1/2, -1/2], [2, 2], [1, 1]]]], [[3, 4, 3, 1, 1], [0 < v, u = -
(v^2+1)^(1/2), And(-1 < x,x < 0), y < x, z < 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [-1/2, -1/2], [-2, -2], [-1, -1]]]], [[3, 4,
3, 1, 2], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y < x, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [-2,
-2], [0, 0]]]], [[3, 4, 3, 1, 3], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0
), y < x, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288],
[-1/2, -1/2], [-2, -2], [1, 1]]]], [[3, 7, 7, 4, 1], [0 < v, And(-v < u,u < v)
, 1 < x, y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
0, 0], [2, 2], [4, 4], [-3, -3]]]], [[3, 7, 7, 4, 2], [0 < v, And(-v < u,u < v
), 1 < x, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[0, 0], [2, 2], [4, 4], [-1482911/1048576, -741455/524288]]]], [[3, 7, 7, 4, 3
], [0 < v, And(-v < u,u < v), 1 < x, y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [2, 2], [4, 4],
[0, 0]]]], [[3, 7, 7, 4, 4], [0 < v, And(-v < u,u < v), 1 < x, y = x-u^2+v^2+1
, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [4, 4], [
741455/524288, 1482911/1048576]]]], [[3, 7, 7, 4, 5], [0 < v, And(-v < u,u < v
), 1 < x, y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [
0, 0], [2, 2], [4, 4], [3, 3]]]], [[1, 4, 1, 2, 1], [v < 0, u = -(v^2+1)^(1/2)
, x < -1, y = x, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455
/524288], [-2, -2], [-2, -2], [-1, -1]]]], [[1, 4, 1, 2, 2], [v < 0, u = -(v^2
+1)^(1/2), x < -1, y = x, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576
, -741455/524288], [-2, -2], [-2, -2], [0, 0]]]], [[1, 4, 1, 2, 3], [v < 0, u
= -(v^2+1)^(1/2), x < -1, y = x, 0 < z], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [-2, -2], [-2, -2], [1, 1]]]], [[1, 7, 5, 5, 1], [v
< 0, And(v < u,u < -v), And(-1 < x,x < 1), x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^
(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [3, 3], [-3, -3]]]], [[1, 7
, 5, 5, 2], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), x-u^2+v^2+1 < y, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [3, 3], [-\
1482911/1048576, -741455/524288]]]], [[1, 7, 5, 5, 3], [v < 0, And(v < u,u < -
v), And(-1 < x,x < 1), x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+
v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [0, 0], [3, 3], [0, 0]]]],
[[1, 7, 5, 5, 4], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), x-u^2+v^2+1 <
y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [3, 3],
[741455/524288, 1482911/1048576]]]], [[1, 7, 5, 5, 5], [v < 0, And(v < u,u < -
v), And(-1 < x,x < 1), x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [0, 0], [0, 0], [3, 3], [3, 3]]]], [[2, 5, 5, 1, 1],
[v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y < u^2-x-1, z < -(-u^2+1)^(1
/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [-2, -2], [-2, -2]]]]
, [[2, 5, 5, 1, 2], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y < u^2-x
-1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [
-2, -2], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 5, 1, 3], [v = 0, 
And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y < u^2-x-1, And(-(-u^2+1)^(1/2) < z,
z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [-2,
-2], [-1/8388608, -1/8388608]]]], [[2, 5, 5, 1, 4], [v = 0, And(-1 < u,u < 0),
And(u^2-1 < x,x < 1), y < u^2-x-1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0
], [-1/2, -1/2], [1/8, 1/8], [-2, -2], [908093/1048576, 454047/524288]]]], [[2
, 5, 5, 1, 5], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y < u^2-x-1, (
-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [-2, -2
], [2, 2]]]], [[2, 9, 2, 2, 1], [v = 0, And(1 < u,u < 2^(1/2)), x = -1, y = -u
^2, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [-1,
-1], [-1527887/1048576, -763943/524288], [0, 0]]]], [[1, 13, 6, 1, 1], [v < 0,
(v^2+2)^(1/2) < u, x = u^2-v^2-1, y < 0, z = z], [regular_chain, [[-1, -1], [3
, 3], [7, 7], [-1, -1], [0, 0]]]], [[2, 4, 3, 4, 1], [v = 0, u = -1, And(-1 <
x,x < 0), y = -x, z < 0], [regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [1/
2, 1/2], [-1, -1]]]], [[2, 4, 3, 4, 2], [v = 0, u = -1, And(-1 < x,x < 0), y =
-x, z = 0], [regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [1/2, 1/2], [0, 0
]]]], [[2, 4, 3, 4, 3], [v = 0, u = -1, And(-1 < x,x < 0), y = -x, 0 < z], [
regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [1/2, 1/2], [1, 1]]]], [[3, 4,
3, 2, 1], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y = x, z < 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [-1/
2, -1/2], [-1, -1]]]], [[3, 4, 3, 2, 2], [0 < v, u = -(v^2+1)^(1/2), And(-1 <
x,x < 0), y = x, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/
524288], [-1/2, -1/2], [-1/2, -1/2], [0, 0]]]], [[3, 4, 3, 2, 3], [0 < v, u =
-(v^2+1)^(1/2), And(-1 < x,x < 0), y = x, 0 < z], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [-1/2, -1/2], [-1/2, -1/2], [1, 1]]]], [[3,
7, 7, 5, 1], [0 < v, And(-v < u,u < v), 1 < x, x-u^2+v^2+1 < y, z < -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [5, 5], [-3, -3]]]], [[3,
7, 7, 5, 2], [0 < v, And(-v < u,u < v), 1 < x, x-u^2+v^2+1 < y, z = -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [5, 5], [-1482911/1048576
, -741455/524288]]]], [[3, 7, 7, 5, 3], [0 < v, And(-v < u,u < v), 1 < x, x-u^
2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [2, 2], [5, 5], [0, 0]]]], [[3, 7, 7, 5, 4], [
0 < v, And(-v < u,u < v), 1 < x, x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [2, 2], [5, 5], [741455/524288, 1482911/
1048576]]]], [[3, 7, 7, 5, 5], [0 < v, And(-v < u,u < v), 1 < x, x-u^2+v^2+1 <
y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [2, 2], [5, 5], [
3, 3]]]], [[1, 4, 1, 1, 1], [v < 0, u = -(v^2+1)^(1/2), x < -1, y < x, z < 0],
[regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-2, -2], [-3,
-3], [-1, -1]]]], [[1, 4, 1, 1, 2], [v < 0, u = -(v^2+1)^(1/2), x < -1, y < x,
z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-2, -2
], [-3, -3], [0, 0]]]], [[1, 4, 1, 1, 3], [v < 0, u = -(v^2+1)^(1/2), x < -1,
y < x, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288],
[-2, -2], [-3, -3], [1, 1]]]], [[1, 7, 5, 4, 1], [v < 0, And(v < u,u < -v), 
And(-1 < x,x < 1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[-1, -1], [0, 0], [0, 0], [2, 2], [-3, -3]]]], [[1, 7, 5, 4, 2], [v < 0, And(
v < u,u < -v), And(-1 < x,x < 1), y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [0, 0], [2, 2], [-1482911/1048576, -741455/
524288]]]], [[1, 7, 5, 4, 3], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), y
= x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [0, 0], [2, 2], [0, 0]]]], [[1, 7, 5, 4, 4],
[v < 0, And(v < u,u < -v), And(-1 < x,x < 1), y = x-u^2+v^2+1, z = (-u^2+v^2+1
)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [2, 2], [741455/524288, 
1482911/1048576]]]], [[1, 7, 5, 4, 5], [v < 0, And(v < u,u < -v), And(-1 < x,x
< 1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0,
0], [0, 0], [2, 2], [3, 3]]]], [[2, 5, 5, 2, 1], [v = 0, And(-1 < u,u < 0), 
And(u^2-1 < x,x < 1), y = u^2-x-1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0,
0], [-1/2, -1/2], [1/8, 1/8], [-7/8, -7/8], [-2, -2]]]], [[2, 5, 5, 2, 2], [v
= 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y = u^2-x-1, z = -(-u^2+1)^(1/2)
], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [-7/8, -7/8], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 5, 2, 3], [v = 0, And(-1 < u,u < 0), 
And(u^2-1 < x,x < 1), y = u^2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))
], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [-7/8, -7/8], [-1/
8388608, -1/8388608]]]], [[2, 5, 5, 2, 4], [v = 0, And(-1 < u,u < 0), And(u^2-\
1 < x,x < 1), y = u^2-x-1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2
, -1/2], [1/8, 1/8], [-7/8, -7/8], [908093/1048576, 454047/524288]]]], [[2, 5,
5, 2, 5], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y = u^2-x-1, (-u^2+
1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [-7/8, -7/8]
, [2, 2]]]], [[2, 9, 2, 3, 1], [v = 0, And(1 < u,u < 2^(1/2)), x = -1, And(-u^
2 < y,y < u^2), z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/
1048576], [-1, -1], [0, 0], [0, 0]]]], [[1, 13, 5, 5, 1], [v < 0, (v^2+2)^(1/2
) < u, And(1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = z], [regular_chain, [[-1
, -1], [3, 3], [4, 4], [4, 4], [0, 0]]]], [[2, 4, 4, 2, 1], [v = 0, u = -1, x
= 0, y = 0, z < 0], [regular_chain, [[0, 0], [-1, -1], [0, 0], [0, 0], [-1, -1
]]]], [[2, 4, 4, 2, 2], [v = 0, u = -1, x = 0, y = 0, z = 0], [regular_chain,
[[0, 0], [-1, -1], [0, 0], [0, 0], [0, 0]]]], [[2, 4, 4, 2, 3], [v = 0, u = -1
, x = 0, y = 0, 0 < z], [regular_chain, [[0, 0], [-1, -1], [0, 0], [0, 0], [1,
1]]]], [[3, 4, 2, 4, 1], [0 < v, u = -(v^2+1)^(1/2), x = -1, y = 1, z < 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1, -1], [1, 1],
[-1, -1]]]], [[3, 4, 2, 4, 2], [0 < v, u = -(v^2+1)^(1/2), x = -1, y = 1, z =
0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1, -1], [1,
1], [0, 0]]]], [[3, 4, 2, 4, 3], [0 < v, u = -(v^2+1)^(1/2), x = -1, y = 1, 0
< z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1, -1], [
1, 1], [1, 1]]]], [[3, 8, 1, 1, 1], [0 < v, u = v, x < -1, y < x+1, z < -1], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [-2, -2], [-2, -2]]]], [[3, 8, 1, 1,
2], [0 < v, u = v, x < -1, y < x+1, z = -1], [regular_chain, [[1, 1], [1, 1],
[-2, -2], [-2, -2], [-1, -1]]]], [[3, 8, 1, 1, 3], [0 < v, u = v, x < -1, y <
x+1, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [-2, -2], [-2, -2],
[0, 0]]]], [[3, 8, 1, 1, 4], [0 < v, u = v, x < -1, y < x+1, z = 1], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [-2, -2], [1, 1]]]], [[3, 8, 1, 1, 5
], [0 < v, u = v, x < -1, y < x+1, 1 < z], [regular_chain, [[1, 1], [1, 1], [-\
2, -2], [-2, -2], [2, 2]]]], [[1, 3, 7, 5, 1], [v < 0, And(-(v^2+2)^(1/2) < u,
u < -(v^2+1)^(1/2)), 1 < x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[-1, -1]
, [-6598195/4194304, -6598195/4194304], [2, 2], [3, 3], [0, 0]]]], [[1, 7, 6,
2, 1], [v < 0, And(v < u,u < -v), x = 1, y = u^2-v^2-2, z < -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[-1, -1], [0, 0], [1, 1], [-3, -3], [-3, -3]]]], [[1, 7,
6, 2, 2], [v < 0, And(v < u,u < -v), x = 1, y = u^2-v^2-2, z = -(-u^2+v^2+1)^(
1/2)], [regular_chain, [[-1, -1], [0, 0], [1, 1], [-3, -3], [-1482911/1048576,
-741455/524288]]]], [[1, 7, 6, 2, 3], [v < 0, And(v < u,u < -v), x = 1, y = u^
2-v^2-2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain,
[[-1, -1], [0, 0], [1, 1], [-3, -3], [0, 0]]]], [[1, 7, 6, 2, 4], [v < 0, And(
v < u,u < -v), x = 1, y = u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain,
[[-1, -1], [0, 0], [1, 1], [-3, -3], [741455/524288, 1482911/1048576]]]], [[1,
7, 6, 2, 5], [v < 0, And(v < u,u < -v), x = 1, y = u^2-v^2-2, (-u^2+v^2+1)^(1/
2) < z], [regular_chain, [[-1, -1], [0, 0], [1, 1], [-3, -3], [3, 3]]]], [[2,
5, 4, 2, 1], [v = 0, And(-1 < u,u < 0), x = u^2-1, y = 0, z < -(-u^2+1)^(1/2)]
, [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [0, 0], [-2, -2]]]], [[
2, 5, 4, 2, 2], [v = 0, And(-1 < u,u < 0), x = u^2-1, y = 0, z = -(-u^2+1)^(1/
2)], [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [0, 0], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 4, 2, 3], [v = 0, And(-1 < u,u < 0), x
= u^2-1, y = 0, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain,
[[0, 0], [-1/2, -1/2], [-3/4, -3/4], [0, 0], [-1/8388608, -1/8388608]]]], [[2,
5, 4, 2, 4], [v = 0, And(-1 < u,u < 0), x = u^2-1, y = 0, z = (-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [0, 0], [908093/1048576,
454047/524288]]]], [[2, 5, 4, 2, 5], [v = 0, And(-1 < u,u < 0), x = u^2-1, y =
0, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [
0, 0], [2, 2]]]], [[2, 9, 2, 4, 1], [v = 0, And(1 < u,u < 2^(1/2)), x = -1, y
= u^2, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [-\
1, -1], [763943/524288, 1527887/1048576], [0, 0]]]], [[1, 13, 5, 4, 1], [v < 0
, (v^2+2)^(1/2) < u, And(1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [3, 3], [4, 4], [3, 3], [0, 0]]]], [[2, 4, 4, 1, 1],
[v = 0, u = -1, x = 0, y < 0, z < 0], [regular_chain, [[0, 0], [-1, -1], [0, 0
], [-1, -1], [-1, -1]]]], [[2, 4, 4, 1, 2], [v = 0, u = -1, x = 0, y < 0, z =
0], [regular_chain, [[0, 0], [-1, -1], [0, 0], [-1, -1], [0, 0]]]], [[2, 4, 4,
1, 3], [v = 0, u = -1, x = 0, y < 0, 0 < z], [regular_chain, [[0, 0], [-1, -1]
, [0, 0], [-1, -1], [1, 1]]]], [[3, 4, 2, 5, 1], [0 < v, u = -(v^2+1)^(1/2), x
= -1, 1 < y, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/
524288], [-1, -1], [2, 2], [-1, -1]]]], [[3, 4, 2, 5, 2], [0 < v, u = -(v^2+1)
^(1/2), x = -1, 1 < y, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [-1, -1], [2, 2], [0, 0]]]], [[3, 4, 2, 5, 3], [0 < v, u = -(v
^2+1)^(1/2), x = -1, 1 < y, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576
, -741455/524288], [-1, -1], [2, 2], [1, 1]]]], [[3, 8, 1, 2, 1], [0 < v, u =
v, x < -1, y = x+1, z < -1], [regular_chain, [[1, 1], [1, 1], [-2, -2], [-1, -\
1], [-2, -2]]]], [[3, 8, 1, 2, 2], [0 < v, u = v, x < -1, y = x+1, z = -1], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [-1, -1], [-1, -1]]]], [[3, 8, 1, 2,
3], [0 < v, u = v, x < -1, y = x+1, And(-1 < z,z < 1)], [regular_chain, [[1, 1
], [1, 1], [-2, -2], [-1, -1], [0, 0]]]], [[3, 8, 1, 2, 4], [0 < v, u = v, x <
-1, y = x+1, z = 1], [regular_chain, [[1, 1], [1, 1], [-2, -2], [-1, -1], [1,
1]]]], [[3, 8, 1, 2, 5], [0 < v, u = v, x < -1, y = x+1, 1 < z], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [-1, -1], [2, 2]]]], [[1, 3, 7, 4, 1
], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), 1 < x, y = x-u^2+v^2+1,
z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [2, 2
], [1599345/1048576, 799673/524288], [0, 0]]]], [[1, 7, 6, 1, 1], [v < 0, And(
v < u,u < -v), x = 1, y < u^2-v^2-2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[-1, -1], [0, 0], [1, 1], [-4, -4], [-3, -3]]]], [[1, 7, 6, 1, 2], [v < 0, 
And(v < u,u < -v), x = 1, y < u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [1, 1], [-4, -4], [-1482911/1048576, -741455
/524288]]]], [[1, 7, 6, 1, 3], [v < 0, And(v < u,u < -v), x = 1, y < u^2-v^2-2
, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1,
-1], [0, 0], [1, 1], [-4, -4], [0, 0]]]], [[1, 7, 6, 1, 4], [v < 0, And(v < u,
u < -v), x = 1, y < u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [0, 0], [1, 1], [-4, -4], [741455/524288, 1482911/1048576]]]], [[1, 7, 6,
1, 5], [v < 0, And(v < u,u < -v), x = 1, y < u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z
], [regular_chain, [[-1, -1], [0, 0], [1, 1], [-4, -4], [3, 3]]]], [[2, 5, 4,
3, 1], [v = 0, And(-1 < u,u < 0), x = u^2-1, 0 < y, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [1, 1], [-2, -2]]]], [[2,
5, 4, 3, 2], [v = 0, And(-1 < u,u < 0), x = u^2-1, 0 < y, z = -(-u^2+1)^(1/2)]
, [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [1, 1], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 4, 3, 3], [v = 0, And(-1 < u,u < 0), x
= u^2-1, 0 < y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain,
[[0, 0], [-1/2, -1/2], [-3/4, -3/4], [1, 1], [-1/8388608, -1/8388608]]]], [[2,
5, 4, 3, 4], [v = 0, And(-1 < u,u < 0), x = u^2-1, 0 < y, z = (-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [1, 1], [908093/1048576,
454047/524288]]]], [[2, 5, 4, 3, 5], [v = 0, And(-1 < u,u < 0), x = u^2-1, 0 <
y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [-3/4, -3/4], [
1, 1], [2, 2]]]], [[2, 9, 2, 5, 1], [v = 0, And(1 < u,u < 2^(1/2)), x = -1, u^
2 < y, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [-\
1, -1], [3, 3], [0, 0]]]], [[1, 4, 2, 1, 1], [v < 0, u = -(v^2+1)^(1/2), x = -\
1, y < -1, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [-1, -1], [-2, -2], [-1, -1]]]], [[1, 4, 2, 1, 2], [v < 0, u = -(v^2+
1)^(1/2), x = -1, y < -1, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576
, -741455/524288], [-1, -1], [-2, -2], [0, 0]]]], [[1, 4, 2, 1, 3], [v < 0, u
= -(v^2+1)^(1/2), x = -1, y < -1, 0 < z], [regular_chain, [[-1, -1], [-1482911
/1048576, -741455/524288], [-1, -1], [-2, -2], [1, 1]]]], [[1, 7, 6, 4, 1], [v
< 0, And(v < u,u < -v), x = 1, y = -u^2+v^2+2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [1, 1], [3, 3], [-3, -3]]]], [[1, 7, 6, 4, 2
], [v < 0, And(v < u,u < -v), x = 1, y = -u^2+v^2+2, z = -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [0, 0], [1, 1], [3, 3], [-1482911/1048576, -741455/
524288]]]], [[1, 7, 6, 4, 3], [v < 0, And(v < u,u < -v), x = 1, y = -u^2+v^2+2
, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1,
-1], [0, 0], [1, 1], [3, 3], [0, 0]]]], [[1, 7, 6, 4, 4], [v < 0, And(v < u,u
< -v), x = 1, y = -u^2+v^2+2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -\
1], [0, 0], [1, 1], [3, 3], [741455/524288, 1482911/1048576]]]], [[1, 7, 6, 4,
5], [v < 0, And(v < u,u < -v), x = 1, y = -u^2+v^2+2, (-u^2+v^2+1)^(1/2) < z],
[regular_chain, [[-1, -1], [0, 0], [1, 1], [3, 3], [3, 3]]]], [[2, 5, 5, 5, 1]
, [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), x-u^2+1 < y, z < -(-u^2+1)^
(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [2, 2], [-2, -2]]]]
, [[2, 5, 5, 5, 2], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), x-u^2+1 <
y, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [2
, 2], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 5, 5, 3], [v = 0, And(-\
1 < u,u < 0), And(u^2-1 < x,x < 1), x-u^2+1 < y, And(-(-u^2+1)^(1/2) < z,z < (
-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [2, 2], [-\
1/8388608, -1/8388608]]]], [[2, 5, 5, 5, 4], [v = 0, And(-1 < u,u < 0), And(u^
2-1 < x,x < 1), x-u^2+1 < y, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1
/2, -1/2], [1/8, 1/8], [2, 2], [908093/1048576, 454047/524288]]]], [[2, 5, 5,
5, 5], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), x-u^2+1 < y, (-u^2+1)^
(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [2, 2], [2, 2]]
]], [[2, 9, 3, 1, 1], [v = 0, And(1 < u,u < 2^(1/2)), And(-1 < x,x < u^2-1), y
< x-u^2+1, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576]
, [-284633/1048576, -284633/1048576], [-2, -2], [0, 0]]]], [[1, 13, 5, 3, 1],
[v < 0, (v^2+2)^(1/2) < u, And(1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u
^2-v^2-x-1), z = z], [regular_chain, [[-1, -1], [3, 3], [4, 4], [0, 0], [0, 0]
]]], [[2, 4, 3, 1, 1], [v = 0, u = -1, And(-1 < x,x < 0), y < x, z < 0], [
regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [-2, -2], [-1, -1]]]], [[2, 4,
3, 1, 2], [v = 0, u = -1, And(-1 < x,x < 0), y < x, z = 0], [regular_chain, [[
0, 0], [-1, -1], [-1/2, -1/2], [-2, -2], [0, 0]]]], [[2, 4, 3, 1, 3], [v = 0,
u = -1, And(-1 < x,x < 0), y < x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [
-1/2, -1/2], [-2, -2], [1, 1]]]], [[3, 4, 2, 2, 1], [0 < v, u = -(v^2+1)^(1/2)
, x = -1, y = -1, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/
524288], [-1, -1], [-1, -1], [-1, -1]]]], [[3, 4, 2, 2, 2], [0 < v, u = -(v^2+
1)^(1/2), x = -1, y = -1, z = 0], [regular_chain, [[1, 1], [-1482911/1048576,
-741455/524288], [-1, -1], [-1, -1], [0, 0]]]], [[3, 4, 2, 2, 3], [0 < v, u =
-(v^2+1)^(1/2), x = -1, y = -1, 0 < z], [regular_chain, [[1, 1], [-1482911/
1048576, -741455/524288], [-1, -1], [-1, -1], [1, 1]]]], [[3, 7, 6, 5, 1], [0
< v, And(-v < u,u < v), x = 1, -u^2+v^2+2 < y, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [1, 1], [4, 4], [-3, -3]]]], [[3, 7, 6, 5, 2],
[0 < v, And(-v < u,u < v), x = 1, -u^2+v^2+2 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [1, 1], [4, 4], [-1482911/1048576, -741455/
524288]]]], [[3, 7, 6, 5, 3], [0 < v, And(-v < u,u < v), x = 1, -u^2+v^2+2 < y
, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1
], [0, 0], [1, 1], [4, 4], [0, 0]]]], [[3, 7, 6, 5, 4], [0 < v, And(-v < u,u <
v), x = 1, -u^2+v^2+2 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
0, 0], [1, 1], [4, 4], [741455/524288, 1482911/1048576]]]], [[3, 7, 6, 5, 5],
[0 < v, And(-v < u,u < v), x = 1, -u^2+v^2+2 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [0, 0], [1, 1], [4, 4], [3, 3]]]], [[1, 4, 1, 5, 1], [
v < 0, u = -(v^2+1)^(1/2), x < -1, -x < y, z < 0], [regular_chain, [[-1, -1],
[-1482911/1048576, -741455/524288], [-2, -2], [3, 3], [-1, -1]]]], [[1, 4, 1,
5, 2], [v < 0, u = -(v^2+1)^(1/2), x < -1, -x < y, z = 0], [regular_chain, [[-\
1, -1], [-1482911/1048576, -741455/524288], [-2, -2], [3, 3], [0, 0]]]], [[1,
4, 1, 5, 3], [v < 0, u = -(v^2+1)^(1/2), x < -1, -x < y, 0 < z], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-2, -2], [3, 3]
, [1, 1]]]], [[1, 7, 6, 3, 1], [v < 0, And(v < u,u < -v), x = 1, And(u^2-v^2-2
< y,y < -u^2+v^2+2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0,
0], [1, 1], [0, 0], [-3, -3]]]], [[1, 7, 6, 3, 2], [v < 0, And(v < u,u < -v),
x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [1, 1], [0, 0], [-1482911/1048576, -741455/
524288]]]], [[1, 7, 6, 3, 3], [v < 0, And(v < u,u < -v), x = 1, And(u^2-v^2-2
< y,y < -u^2+v^2+2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [1, 1], [0, 0], [0, 0]]]], [[1, 7, 6, 3, 4],
[v < 0, And(v < u,u < -v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = (-u^2
+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [1, 1], [0, 0], [741455/
524288, 1482911/1048576]]]], [[1, 7, 6, 3, 5], [v < 0, And(v < u,u < -v), x =
1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[-1, -1], [0, 0], [1, 1], [0, 0], [3, 3]]]], [[2, 5, 6, 1, 1], [v = 0, And(-1
< u,u < 0), x = 1, y < u^2-2, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [
-1/2, -1/2], [1, 1], [-3, -3], [-2, -2]]]], [[2, 5, 6, 1, 2], [v = 0, And(-1 <
u,u < 0), x = 1, y < u^2-2, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1
/2, -1/2], [1, 1], [-3, -3], [-1816187/2097152, -3632373/4194304]]]], [[2, 5,
6, 1, 3], [v = 0, And(-1 < u,u < 0), x = 1, y < u^2-2, And(-(-u^2+1)^(1/2) < z
,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [-3, -3]
, [-1/8388608, -1/8388608]]]], [[2, 5, 6, 1, 4], [v = 0, And(-1 < u,u < 0), x
= 1, y < u^2-2, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1
, 1], [-3, -3], [908093/1048576, 454047/524288]]]], [[2, 5, 6, 1, 5], [v = 0,
And(-1 < u,u < 0), x = 1, y < u^2-2, (-u^2+1)^(1/2) < z], [regular_chain, [[0,
0], [-1/2, -1/2], [1, 1], [-3, -3], [2, 2]]]], [[2, 9, 3, 2, 1], [v = 0, And(1
< u,u < 2^(1/2)), And(-1 < x,x < u^2-1), y = x-u^2+1, z = z], [regular_chain,
[[0, 0], [1265743/1048576, 1265743/1048576], [-284633/1048576, -284633/1048576
], [-95493/131072, -1527887/2097152], [0, 0]]]], [[1, 13, 5, 2, 1], [v < 0, (v
^2+2)^(1/2) < u, And(1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [3, 3], [4, 4], [-3, -3], [0, 0]]]], [[2, 4, 2, 5, 1
], [v = 0, u = -1, x = -1, 1 < y, z < 0], [regular_chain, [[0, 0], [-1, -1], [
-1, -1], [2, 2], [-1, -1]]]], [[2, 4, 2, 5, 2], [v = 0, u = -1, x = -1, 1 < y,
z = 0], [regular_chain, [[0, 0], [-1, -1], [-1, -1], [2, 2], [0, 0]]]], [[2, 4
, 2, 5, 3], [v = 0, u = -1, x = -1, 1 < y, 0 < z], [regular_chain, [[0, 0], [-\
1, -1], [-1, -1], [2, 2], [1, 1]]]], [[3, 4, 2, 3, 1], [0 < v, u = -(v^2+1)^(1
/2), x = -1, And(-1 < y,y < 1), z < 0], [regular_chain, [[1, 1], [-1482911/
1048576, -741455/524288], [-1, -1], [0, 0], [-1, -1]]]], [[3, 4, 2, 3, 2], [0
< v, u = -(v^2+1)^(1/2), x = -1, And(-1 < y,y < 1), z = 0], [regular_chain, [[
1, 1], [-1482911/1048576, -741455/524288], [-1, -1], [0, 0], [0, 0]]]], [[3, 4
, 2, 3, 3], [0 < v, u = -(v^2+1)^(1/2), x = -1, And(-1 < y,y < 1), 0 < z], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1, -1], [0, 0],
[1, 1]]]], [[3, 7, 7, 1, 1], [0 < v, And(-v < u,u < v), 1 < x, y < u^2-v^2-x-1
, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [-5, -5],
[-3, -3]]]], [[3, 7, 7, 1, 2], [0 < v, And(-v < u,u < v), 1 < x, y < u^2-v^2-x
-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [-5, -5
], [-1482911/1048576, -741455/524288]]]], [[3, 7, 7, 1, 3], [0 < v, And(-v < u
,u < v), 1 < x, y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^
(1/2))], [regular_chain, [[1, 1], [0, 0], [2, 2], [-5, -5], [0, 0]]]], [[3, 7,
7, 1, 4], [0 < v, And(-v < u,u < v), 1 < x, y < u^2-v^2-x-1, z = (-u^2+v^2+1)^
(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [-5, -5], [741455/524288, 
1482911/1048576]]]], [[3, 7, 7, 1, 5], [0 < v, And(-v < u,u < v), 1 < x, y < u
^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [2, 2],
[-5, -5], [3, 3]]]], [[1, 4, 1, 4, 1], [v < 0, u = -(v^2+1)^(1/2), x < -1, y =
-x, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-2
, -2], [2, 2], [-1, -1]]]], [[1, 4, 1, 4, 2], [v < 0, u = -(v^2+1)^(1/2), x <
-1, y = -x, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [-2, -2], [2, 2], [0, 0]]]], [[1, 4, 1, 4, 3], [v < 0, u = -(v^2+1)^(
1/2), x < -1, y = -x, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -\
741455/524288], [-2, -2], [2, 2], [1, 1]]]], [[1, 7, 7, 1, 1], [v < 0, And(v <
u,u < -v), 1 < x, y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [0, 0], [2, 2], [-5, -5], [-3, -3]]]], [[1, 7, 7, 1, 2], [v < 0, And
(v < u,u < -v), 1 < x, y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [2, 2], [-5, -5], [-1482911/1048576, -741455
/524288]]]], [[1, 7, 7, 1, 3], [v < 0, And(v < u,u < -v), 1 < x, y < u^2-v^2-x
-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1
, -1], [0, 0], [2, 2], [-5, -5], [0, 0]]]], [[1, 7, 7, 1, 4], [v < 0, And(v <
u,u < -v), 1 < x, y < u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
-1, -1], [0, 0], [2, 2], [-5, -5], [741455/524288, 1482911/1048576]]]], [[1, 7
, 7, 1, 5], [v < 0, And(v < u,u < -v), 1 < x, y < u^2-v^2-x-1, (-u^2+v^2+1)^(1
/2) < z], [regular_chain, [[-1, -1], [0, 0], [2, 2], [-5, -5], [3, 3]]]], [[2,
5, 5, 3, 1], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,
y < x-u^2+1), z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1/
8, 1/8], [0, 0], [-2, -2]]]], [[2, 5, 5, 3, 2], [v = 0, And(-1 < u,u < 0), And
(u^2-1 < x,x < 1), And(u^2-x-1 < y,y < x-u^2+1), z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [0, 0], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 5, 5, 3, 3], [v = 0, And(-1 < u,u < 0), And(u^2-1 <
x,x < 1), And(u^2-x-1 < y,y < x-u^2+1), And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(
1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [0, 0], [-1/8388608
, -1/8388608]]]], [[2, 5, 5, 3, 4], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x
< 1), And(u^2-x-1 < y,y < x-u^2+1), z = (-u^2+1)^(1/2)], [regular_chain, [[0,
0], [-1/2, -1/2], [1/8, 1/8], [0, 0], [908093/1048576, 454047/524288]]]], [[2,
5, 5, 3, 5], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,
y < x-u^2+1), (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8
, 1/8], [0, 0], [2, 2]]]], [[2, 9, 3, 3, 1], [v = 0, And(1 < u,u < 2^(1/2)), 
And(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), z = z], [regular_chain, [
[0, 0], [1265743/1048576, 1265743/1048576], [-284633/1048576, -284633/1048576]
, [-1/4194304, -1/4194304], [0, 0]]]], [[1, 13, 5, 1, 1], [v < 0, (v^2+2)^(1/2
) < u, And(1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = z], [regular_chain, [[-1
, -1], [3, 3], [4, 4], [-4, -4], [0, 0]]]], [[2, 4, 3, 3, 1], [v = 0, u = -1,
And(-1 < x,x < 0), And(x < y,y < -x), z < 0], [regular_chain, [[0, 0], [-1, -1
], [-1/2, -1/2], [0, 0], [-1, -1]]]], [[2, 4, 3, 3, 2], [v = 0, u = -1, And(-1
< x,x < 0), And(x < y,y < -x), z = 0], [regular_chain, [[0, 0], [-1, -1], [-1/
2, -1/2], [0, 0], [0, 0]]]], [[2, 4, 3, 3, 3], [v = 0, u = -1, And(-1 < x,x <
0), And(x < y,y < -x), 0 < z], [regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2]
, [0, 0], [1, 1]]]], [[3, 4, 1, 5, 1], [0 < v, u = -(v^2+1)^(1/2), x < -1, -x
< y, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-2,
-2], [3, 3], [-1, -1]]]], [[3, 4, 1, 5, 2], [0 < v, u = -(v^2+1)^(1/2), x < -1
, -x < y, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288],
[-2, -2], [3, 3], [0, 0]]]], [[3, 4, 1, 5, 3], [0 < v, u = -(v^2+1)^(1/2), x <
-1, -x < y, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288
], [-2, -2], [3, 3], [1, 1]]]], [[3, 7, 7, 2, 1], [0 < v, And(-v < u,u < v), 1
< x, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0
], [2, 2], [-4, -4], [-3, -3]]]], [[3, 7, 7, 2, 2], [0 < v, And(-v < u,u < v),
1 < x, y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0,
0], [2, 2], [-4, -4], [-1482911/1048576, -741455/524288]]]], [[3, 7, 7, 2, 3],
[0 < v, And(-v < u,u < v), 1 < x, y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z
,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [2, 2], [-4, -4],
[0, 0]]]], [[3, 7, 7, 2, 4], [0 < v, And(-v < u,u < v), 1 < x, y = u^2-v^2-x-1
, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [-4, -4],
[741455/524288, 1482911/1048576]]]], [[3, 7, 7, 2, 5], [0 < v, And(-v < u,u <
v), 1 < x, y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1],
[0, 0], [2, 2], [-4, -4], [3, 3]]]], [[1, 4, 1, 3, 1], [v < 0, u = -(v^2+1)^(1
/2), x < -1, And(x < y,y < -x), z < 0], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [-2, -2], [0, 0], [-1, -1]]]], [[1, 4, 1, 3, 2], [v
< 0, u = -(v^2+1)^(1/2), x < -1, And(x < y,y < -x), z = 0], [regular_chain, [[
-1, -1], [-1482911/1048576, -741455/524288], [-2, -2], [0, 0], [0, 0]]]], [[1,
4, 1, 3, 3], [v < 0, u = -(v^2+1)^(1/2), x < -1, And(x < y,y < -x), 0 < z], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-2, -2], [0, 0]
, [1, 1]]]], [[1, 7, 6, 5, 1], [v < 0, And(v < u,u < -v), x = 1, -u^2+v^2+2 <
y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [1, 1], [4, 4]
, [-3, -3]]]], [[1, 7, 6, 5, 2], [v < 0, And(v < u,u < -v), x = 1, -u^2+v^2+2
< y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [1, 1], [4,
4], [-1482911/1048576, -741455/524288]]]], [[1, 7, 6, 5, 3], [v < 0, And(v < u
,u < -v), x = 1, -u^2+v^2+2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^
(1/2))], [regular_chain, [[-1, -1], [0, 0], [1, 1], [4, 4], [0, 0]]]], [[1, 7,
6, 5, 4], [v < 0, And(v < u,u < -v), x = 1, -u^2+v^2+2 < y, z = (-u^2+v^2+1)^(
1/2)], [regular_chain, [[-1, -1], [0, 0], [1, 1], [4, 4], [741455/524288, 
1482911/1048576]]]], [[1, 7, 6, 5, 5], [v < 0, And(v < u,u < -v), x = 1, -u^2+
v^2+2 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [1, 1],
[4, 4], [3, 3]]]], [[2, 5, 5, 4, 1], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,
x < 1), y = x-u^2+1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/
2], [1/8, 1/8], [7/8, 7/8], [-2, -2]]]], [[2, 5, 5, 4, 2], [v = 0, And(-1 < u,
u < 0), And(u^2-1 < x,x < 1), y = x-u^2+1, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [7/8, 7/8], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 5, 4, 3], [v = 0, And(-1 < u,u < 0), 
And(u^2-1 < x,x < 1), y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))
], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [7/8, 7/8], [-1/8388608,
-1/8388608]]]], [[2, 5, 5, 4, 4], [v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x <
1), y = x-u^2+1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [
1/8, 1/8], [7/8, 7/8], [908093/1048576, 454047/524288]]]], [[2, 5, 5, 4, 5], [
v = 0, And(-1 < u,u < 0), And(u^2-1 < x,x < 1), y = x-u^2+1, (-u^2+1)^(1/2) <
z], [regular_chain, [[0, 0], [-1/2, -1/2], [1/8, 1/8], [7/8, 7/8], [2, 2]]]],
[[2, 9, 3, 4, 1], [v = 0, And(1 < u,u < 2^(1/2)), And(-1 < x,x < u^2-1), y = u
^2-x-1, z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [
-284633/1048576, -284633/1048576], [763943/1048576, 95493/131072], [0, 0]]]],
[[1, 13, 4, 5, 1], [v < 0, (v^2+2)^(1/2) < u, x = 1, u^2-v^2-2 < y, z = z], [
regular_chain, [[-1, -1], [3, 3], [1, 1], [7, 7], [0, 0]]]], [[2, 4, 3, 2, 1],
[v = 0, u = -1, And(-1 < x,x < 0), y = x, z < 0], [regular_chain, [[0, 0], [-1
, -1], [-1/2, -1/2], [-1/2, -1/2], [-1, -1]]]], [[2, 4, 3, 2, 2], [v = 0, u =
-1, And(-1 < x,x < 0), y = x, z = 0], [regular_chain, [[0, 0], [-1, -1], [-1/2
, -1/2], [-1/2, -1/2], [0, 0]]]], [[2, 4, 3, 2, 3], [v = 0, u = -1, And(-1 < x
,x < 0), y = x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [-1/2, -1/2], [-1/2
, -1/2], [1, 1]]]], [[3, 4, 2, 1, 1], [0 < v, u = -(v^2+1)^(1/2), x = -1, y <
-1, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1,
-1], [-2, -2], [-1, -1]]]], [[3, 4, 2, 1, 2], [0 < v, u = -(v^2+1)^(1/2), x =
-1, y < -1, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288
], [-1, -1], [-2, -2], [0, 0]]]], [[3, 4, 2, 1, 3], [0 < v, u = -(v^2+1)^(1/2)
, x = -1, y < -1, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/
524288], [-1, -1], [-2, -2], [1, 1]]]], [[3, 7, 7, 3, 1], [0 < v, And(-v < u,u
< v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [2, 2], [0, 0], [-3, -3]]]], [[3, 7, 7, 3, 2],
[0 < v, And(-v < u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(
-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [0, 0], [-1482911
/1048576, -741455/524288]]]], [[3, 7, 7, 3, 3], [0 < v, And(-v < u,u < v), 1 <
x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2
+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [2, 2], [0, 0], [0, 0]]]], [
[3, 7, 7, 3, 4], [0 < v, And(-v < u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u
^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [2, 2], [
0, 0], [741455/524288, 1482911/1048576]]]], [[3, 7, 7, 3, 5], [0 < v, And(-v <
u,u < v), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z]
, [regular_chain, [[1, 1], [0, 0], [2, 2], [0, 0], [3, 3]]]], [[1, 13, 4, 3, 1
], [v < 0, (v^2+2)^(1/2) < u, x = 1, And(-u^2+v^2+2 < y,y < u^2-v^2-2), z = z]
, [regular_chain, [[-1, -1], [3, 3], [1, 1], [0, 0], [0, 0]]]], [[2, 4, 2, 1,
1], [v = 0, u = -1, x = -1, y < -1, z < 0], [regular_chain, [[0, 0], [-1, -1],
[-1, -1], [-2, -2], [-1, -1]]]], [[2, 4, 2, 1, 2], [v = 0, u = -1, x = -1, y <
-1, z = 0], [regular_chain, [[0, 0], [-1, -1], [-1, -1], [-2, -2], [0, 0]]]],
[[2, 4, 2, 1, 3], [v = 0, u = -1, x = -1, y < -1, 0 < z], [regular_chain, [[0,
0], [-1, -1], [-1, -1], [-2, -2], [1, 1]]]], [[3, 4, 5, 2, 1], [0 < v, u = -(v
^2+1)^(1/2), And(0 < x,x < 1), y = -x, z < 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [1/2, 1/2], [-1/2, -1/2], [-1, -1]]]], [[3,
4, 5, 2, 2], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y = -x, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [-1/2,
-1/2], [0, 0]]]], [[3, 4, 5, 2, 3], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x <
1), y = -x, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288
], [1/2, 1/2], [-1/2, -1/2], [1, 1]]]], [[3, 8, 2, 3, 1], [0 < v, u = v, x = -\
1, 0 < y, z < -1], [regular_chain, [[1, 1], [1, 1], [-1, -1], [1, 1], [-2, -2]
]]], [[3, 8, 2, 3, 2], [0 < v, u = v, x = -1, 0 < y, z = -1], [regular_chain,
[[1, 1], [1, 1], [-1, -1], [1, 1], [-1, -1]]]], [[3, 8, 2, 3, 3], [0 < v, u =
v, x = -1, 0 < y, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [-1, -1
], [1, 1], [0, 0]]]], [[3, 8, 2, 3, 4], [0 < v, u = v, x = -1, 0 < y, z = 1],
[regular_chain, [[1, 1], [1, 1], [-1, -1], [1, 1], [1, 1]]]], [[3, 8, 2, 3, 5]
, [0 < v, u = v, x = -1, 0 < y, 1 < z], [regular_chain, [[1, 1], [1, 1], [-1,
-1], [1, 1], [2, 2]]]], [[1, 3, 6, 3, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -
(v^2+1)^(1/2)), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [1, 1], [-1/
4194304, -1/4194304], [0, 0]]]], [[1, 7, 4, 1, 1], [v < 0, And(v < u,u < -v),
x = -1, y < u^2-v^2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0,
0], [-1, -1], [-2, -2], [-3, -3]]]], [[1, 7, 4, 1, 2], [v < 0, And(v < u,u < -
v), x = -1, y < u^2-v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1],
[0, 0], [-1, -1], [-2, -2], [-1482911/1048576, -741455/524288]]]], [[1, 7, 4,
1, 3], [v < 0, And(v < u,u < -v), x = -1, y < u^2-v^2, And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [-2
, -2], [0, 0]]]], [[1, 7, 4, 1, 4], [v < 0, And(v < u,u < -v), x = -1, y < u^2
-v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [-\
2, -2], [741455/524288, 1482911/1048576]]]], [[1, 7, 4, 1, 5], [v < 0, And(v <
u,u < -v), x = -1, y < u^2-v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1,
-1], [0, 0], [-1, -1], [-2, -2], [3, 3]]]], [[2, 5, 6, 5, 1], [v = 0, And(-1 <
u,u < 0), x = 1, -u^2+2 < y, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-\
1/2, -1/2], [1, 1], [3, 3], [-2, -2]]]], [[2, 5, 6, 5, 2], [v = 0, And(-1 < u,
u < 0), x = 1, -u^2+2 < y, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/
2, -1/2], [1, 1], [3, 3], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 6,
5, 3], [v = 0, And(-1 < u,u < 0), x = 1, -u^2+2 < y, And(-(-u^2+1)^(1/2) < z,z
< (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [3, 3], [-1
/8388608, -1/8388608]]]], [[2, 5, 6, 5, 4], [v = 0, And(-1 < u,u < 0), x = 1,
-u^2+2 < y, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1]
, [3, 3], [908093/1048576, 454047/524288]]]], [[2, 5, 6, 5, 5], [v = 0, And(-1
< u,u < 0), x = 1, -u^2+2 < y, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [
-1/2, -1/2], [1, 1], [3, 3], [2, 2]]]], [[2, 9, 4, 1, 1], [v = 0, And(1 < u,u
< 2^(1/2)), x = u^2-1, y < 0, z = z], [regular_chain, [[0, 0], [1265743/
1048576, 1265743/1048576], [239655/524288, 479311/1048576], [-1, -1], [0, 0]]]
], [[3, 13, 6, 3, 1], [0 < v, (v^2+2)^(1/2) < u, x = u^2-v^2-1, 0 < y, z = z],
[regular_chain, [[1, 1], [3, 3], [7, 7], [1, 1], [0, 0]]]], [[1, 13, 4, 4, 1],
[v < 0, (v^2+2)^(1/2) < u, x = 1, y = u^2-v^2-2, z = z], [regular_chain, [[-1,
-1], [3, 3], [1, 1], [6, 6], [0, 0]]]], [[2, 4, 2, 2, 1], [v = 0, u = -1, x =
-1, y = -1, z < 0], [regular_chain, [[0, 0], [-1, -1], [-1, -1], [-1, -1], [-1
, -1]]]], [[2, 4, 2, 2, 2], [v = 0, u = -1, x = -1, y = -1, z = 0], [
regular_chain, [[0, 0], [-1, -1], [-1, -1], [-1, -1], [0, 0]]]], [[2, 4, 2, 2,
3], [v = 0, u = -1, x = -1, y = -1, 0 < z], [regular_chain, [[0, 0], [-1, -1],
[-1, -1], [-1, -1], [1, 1]]]], [[3, 4, 5, 1, 1], [0 < v, u = -(v^2+1)^(1/2), 
And(0 < x,x < 1), y < -x, z < 0], [regular_chain, [[1, 1], [-1482911/1048576,
-741455/524288], [1/2, 1/2], [-2, -2], [-1, -1]]]], [[3, 4, 5, 1, 2], [0 < v,
u = -(v^2+1)^(1/2), And(0 < x,x < 1), y < -x, z = 0], [regular_chain, [[1, 1],
[-1482911/1048576, -741455/524288], [1/2, 1/2], [-2, -2], [0, 0]]]], [[3, 4, 5
, 1, 3], [0 < v, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y < -x, 0 < z], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [-2, -\
2], [1, 1]]]], [[3, 8, 2, 2, 1], [0 < v, u = v, x = -1, y = 0, z < -1], [
regular_chain, [[1, 1], [1, 1], [-1, -1], [0, 0], [-2, -2]]]], [[3, 8, 2, 2, 2
], [0 < v, u = v, x = -1, y = 0, z = -1], [regular_chain, [[1, 1], [1, 1], [-1
, -1], [0, 0], [-1, -1]]]], [[3, 8, 2, 2, 3], [0 < v, u = v, x = -1, y = 0, 
And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [-1, -1], [0, 0], [0, 0]]
]], [[3, 8, 2, 2, 4], [0 < v, u = v, x = -1, y = 0, z = 1], [regular_chain, [[
1, 1], [1, 1], [-1, -1], [0, 0], [1, 1]]]], [[3, 8, 2, 2, 5], [0 < v, u = v, x
= -1, y = 0, 1 < z], [regular_chain, [[1, 1], [1, 1], [-1, -1], [0, 0], [2, 2]
]]], [[1, 3, 6, 4, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x =
1, y = -u^2+v^2+2, z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -\
6598195/4194304], [1, 1], [550769/1048576, 275385/524288], [0, 0]]]], [[1, 7,
4, 2, 1], [v < 0, And(v < u,u < -v), x = -1, y = u^2-v^2, z < -(-u^2+v^2+1)^(1
/2)], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [-1, -1], [-3, -3]]]], [[1,
7, 4, 2, 2], [v < 0, And(v < u,u < -v), x = -1, y = u^2-v^2, z = -(-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [-1, -1], [-1482911/
1048576, -741455/524288]]]], [[1, 7, 4, 2, 3], [v < 0, And(v < u,u < -v), x =
-1, y = u^2-v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [-1, -1], [-1, -1], [0, 0]]]], [[1, 7, 4, 2,
4], [v < 0, And(v < u,u < -v), x = -1, y = u^2-v^2, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-1, -1], [-1, -1], [741455/524288, 1482911/
1048576]]]], [[1, 7, 4, 2, 5], [v < 0, And(v < u,u < -v), x = -1, y = u^2-v^2,
(-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [-1, -1]
, [3, 3]]]], [[2, 5, 6, 4, 1], [v = 0, And(-1 < u,u < 0), x = 1, y = -u^2+2, z
< -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [7/4, 7/4],
[-2, -2]]]], [[2, 5, 6, 4, 2], [v = 0, And(-1 < u,u < 0), x = 1, y = -u^2+2, z
= -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [7/4, 7/4],
[-1816187/2097152, -3632373/4194304]]]], [[2, 5, 6, 4, 3], [v = 0, And(-1 < u,
u < 0), x = 1, y = -u^2+2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [7/4, 7/4], [-1/8388608, -1/
8388608]]]], [[2, 5, 6, 4, 4], [v = 0, And(-1 < u,u < 0), x = 1, y = -u^2+2, z
= (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [7/4, 7/4],
[908093/1048576, 454047/524288]]]], [[2, 5, 6, 4, 5], [v = 0, And(-1 < u,u < 0
), x = 1, y = -u^2+2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/
2], [1, 1], [7/4, 7/4], [2, 2]]]], [[2, 9, 3, 5, 1], [v = 0, And(1 < u,u < 2^(
1/2)), And(-1 < x,x < u^2-1), u^2-x-1 < y, z = z], [regular_chain, [[0, 0], [
1265743/1048576, 1265743/1048576], [-284633/1048576, -284633/1048576], [2, 2],
[0, 0]]]], [[3, 13, 7, 1, 1], [0 < v, (v^2+2)^(1/2) < u, u^2-v^2-1 < x, y < u^
2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3, 3], [8, 8], [-2, -2], [0, 0]]]
], [[1, 13, 4, 1, 1], [v < 0, (v^2+2)^(1/2) < u, x = 1, y < -u^2+v^2+2, z = z]
, [regular_chain, [[-1, -1], [3, 3], [1, 1], [-7, -7], [0, 0]]]], [[2, 4, 2, 3
, 1], [v = 0, u = -1, x = -1, And(-1 < y,y < 1), z < 0], [regular_chain, [[0,
0], [-1, -1], [-1, -1], [0, 0], [-1, -1]]]], [[2, 4, 2, 3, 2], [v = 0, u = -1,
x = -1, And(-1 < y,y < 1), z = 0], [regular_chain, [[0, 0], [-1, -1], [-1, -1]
, [0, 0], [0, 0]]]], [[2, 4, 2, 3, 3], [v = 0, u = -1, x = -1, And(-1 < y,y <
1), 0 < z], [regular_chain, [[0, 0], [-1, -1], [-1, -1], [0, 0], [1, 1]]]], [[
3, 4, 4, 3, 1], [0 < v, u = -(v^2+1)^(1/2), x = 0, 0 < y, z < 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [0, 0], [1, 1], [-\
1, -1]]]], [[3, 4, 4, 3, 2], [0 < v, u = -(v^2+1)^(1/2), x = 0, 0 < y, z = 0],
[regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [0, 0], [1, 1], [
0, 0]]]], [[3, 4, 4, 3, 3], [0 < v, u = -(v^2+1)^(1/2), x = 0, 0 < y, 0 < z],
[regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [0, 0], [1, 1], [
1, 1]]]], [[3, 8, 3, 2, 1], [0 < v, u = v, And(-1 < x,x < 1), y = -1-x, z < -1
], [regular_chain, [[1, 1], [1, 1], [0, 0], [-1, -1], [-2, -2]]]], [[3, 8, 3,
2, 2], [0 < v, u = v, And(-1 < x,x < 1), y = -1-x, z = -1], [regular_chain, [[
1, 1], [1, 1], [0, 0], [-1, -1], [-1, -1]]]], [[3, 8, 3, 2, 3], [0 < v, u = v,
And(-1 < x,x < 1), y = -1-x, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1,
1], [0, 0], [-1, -1], [0, 0]]]], [[3, 8, 3, 2, 4], [0 < v, u = v, And(-1 < x,x
< 1), y = -1-x, z = 1], [regular_chain, [[1, 1], [1, 1], [0, 0], [-1, -1], [1,
1]]]], [[3, 8, 3, 2, 5], [0 < v, u = v, And(-1 < x,x < 1), y = -1-x, 1 < z], [
regular_chain, [[1, 1], [1, 1], [0, 0], [-1, -1], [2, 2]]]], [[1, 3, 6, 1, 1],
[v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = 1, y < u^2-v^2-2, z =
z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [1, 1], [
-2, -2], [0, 0]]]], [[1, 7, 4, 3, 1], [v < 0, And(v < u,u < -v), x = -1, And(u
^2-v^2 < y,y < -u^2+v^2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1],
[0, 0], [-1, -1], [0, 0], [-3, -3]]]], [[1, 7, 4, 3, 2], [v < 0, And(v < u,u <
-v), x = -1, And(u^2-v^2 < y,y < -u^2+v^2), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [0, 0], [-1, -1], [0, 0], [-1482911/1048576, -741455
/524288]]]], [[1, 7, 4, 3, 3], [v < 0, And(v < u,u < -v), x = -1, And(u^2-v^2
< y,y < -u^2+v^2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [-1, -1], [0, 0], [0, 0]]]], [[1, 7, 4, 3, 4
], [v < 0, And(v < u,u < -v), x = -1, And(u^2-v^2 < y,y < -u^2+v^2), z = (-u^2
+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [0, 0], [741455/
524288, 1482911/1048576]]]], [[1, 7, 4, 3, 5], [v < 0, And(v < u,u < -v), x =
-1, And(u^2-v^2 < y,y < -u^2+v^2), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[
-1, -1], [0, 0], [-1, -1], [0, 0], [3, 3]]]], [[2, 5, 6, 3, 1], [v = 0, And(-1
< u,u < 0), x = 1, And(u^2-2 < y,y < -u^2+2), z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [0, 0], [-2, -2]]]], [[2, 5, 6,
3, 2], [v = 0, And(-1 < u,u < 0), x = 1, And(u^2-2 < y,y < -u^2+2), z = -(-u^2
+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [0, 0], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 6, 3, 3], [v = 0, And(-1 < u,u < 0), x
= 1, And(u^2-2 < y,y < -u^2+2), And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))],
[regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [0, 0], [-1/8388608, -1/8388608
]]]], [[2, 5, 6, 3, 4], [v = 0, And(-1 < u,u < 0), x = 1, And(u^2-2 < y,y < -u
^2+2), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [0,
0], [908093/1048576, 454047/524288]]]], [[2, 5, 6, 3, 5], [v = 0, And(-1 < u,u
< 0), x = 1, And(u^2-2 < y,y < -u^2+2), (-u^2+1)^(1/2) < z], [regular_chain, [
[0, 0], [-1/2, -1/2], [1, 1], [0, 0], [2, 2]]]], [[2, 9, 4, 3, 1], [v = 0, And
(1 < u,u < 2^(1/2)), x = u^2-1, 0 < y, z = z], [regular_chain, [[0, 0], [
1265743/1048576, 1265743/1048576], [239655/524288, 479311/1048576], [1, 1], [0
, 0]]]], [[3, 13, 6, 1, 1], [0 < v, (v^2+2)^(1/2) < u, x = u^2-v^2-1, y < 0, z
= z], [regular_chain, [[1, 1], [3, 3], [7, 7], [-1, -1], [0, 0]]]], [[1, 13, 4
, 2, 1], [v < 0, (v^2+2)^(1/2) < u, x = 1, y = -u^2+v^2+2, z = z], [
regular_chain, [[-1, -1], [3, 3], [1, 1], [-6, -6], [0, 0]]]], [[2, 4, 2, 4, 1
], [v = 0, u = -1, x = -1, y = 1, z < 0], [regular_chain, [[0, 0], [-1, -1], [
-1, -1], [1, 1], [-1, -1]]]], [[2, 4, 2, 4, 2], [v = 0, u = -1, x = -1, y = 1,
z = 0], [regular_chain, [[0, 0], [-1, -1], [-1, -1], [1, 1], [0, 0]]]], [[2, 4
, 2, 4, 3], [v = 0, u = -1, x = -1, y = 1, 0 < z], [regular_chain, [[0, 0], [-\
1, -1], [-1, -1], [1, 1], [1, 1]]]], [[3, 4, 4, 2, 1], [0 < v, u = -(v^2+1)^(1
/2), x = 0, y = 0, z < 0], [regular_chain, [[1, 1], [-1482911/1048576, -741455
/524288], [0, 0], [0, 0], [-1, -1]]]], [[3, 4, 4, 2, 2], [0 < v, u = -(v^2+1)^
(1/2), x = 0, y = 0, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [0, 0], [0, 0], [0, 0]]]], [[3, 4, 4, 2, 3], [0 < v, u = -(v^2
+1)^(1/2), x = 0, y = 0, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [0, 0], [0, 0], [1, 1]]]], [[3, 8, 3, 1, 1], [0 < v, u = v, 
And(-1 < x,x < 1), y < -1-x, z < -1], [regular_chain, [[1, 1], [1, 1], [0, 0],
[-2, -2], [-2, -2]]]], [[3, 8, 3, 1, 2], [0 < v, u = v, And(-1 < x,x < 1), y <
-1-x, z = -1], [regular_chain, [[1, 1], [1, 1], [0, 0], [-2, -2], [-1, -1]]]],
[[3, 8, 3, 1, 3], [0 < v, u = v, And(-1 < x,x < 1), y < -1-x, And(-1 < z,z < 1
)], [regular_chain, [[1, 1], [1, 1], [0, 0], [-2, -2], [0, 0]]]], [[3, 8, 3, 1
, 4], [0 < v, u = v, And(-1 < x,x < 1), y < -1-x, z = 1], [regular_chain, [[1,
1], [1, 1], [0, 0], [-2, -2], [1, 1]]]], [[3, 8, 3, 1, 5], [0 < v, u = v, And(
-1 < x,x < 1), y < -1-x, 1 < z], [regular_chain, [[1, 1], [1, 1], [0, 0], [-2,
-2], [2, 2]]]], [[1, 3, 6, 2, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^
(1/2)), x = 1, y = u^2-v^2-2, z = z], [regular_chain, [[-1, -1], [-6598195/
4194304, -6598195/4194304], [1, 1], [-275385/524288, -1101539/2097152], [0, 0]
]]], [[1, 7, 4, 4, 1], [v < 0, And(v < u,u < -v), x = -1, y = -u^2+v^2, z < -(
-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [1, 1], [-3,
-3]]]], [[1, 7, 4, 4, 2], [v < 0, And(v < u,u < -v), x = -1, y = -u^2+v^2, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [1, 1], [-\
1482911/1048576, -741455/524288]]]], [[1, 7, 4, 4, 3], [v < 0, And(v < u,u < -
v), x = -1, y = -u^2+v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))]
, [regular_chain, [[-1, -1], [0, 0], [-1, -1], [1, 1], [0, 0]]]], [[1, 7, 4, 4
, 4], [v < 0, And(v < u,u < -v), x = -1, y = -u^2+v^2, z = (-u^2+v^2+1)^(1/2)]
, [regular_chain, [[-1, -1], [0, 0], [-1, -1], [1, 1], [741455/524288, 1482911
/1048576]]]], [[1, 7, 4, 4, 5], [v < 0, And(v < u,u < -v), x = -1, y = -u^2+v^
2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [0, 0], [-1, -1], [1, 1
], [3, 3]]]], [[2, 5, 6, 2, 1], [v = 0, And(-1 < u,u < 0), x = 1, y = u^2-2, z
< -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [-7/4, -7/4
], [-2, -2]]]], [[2, 5, 6, 2, 2], [v = 0, And(-1 < u,u < 0), x = 1, y = u^2-2,
z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [-7/4, -7
/4], [-1816187/2097152, -3632373/4194304]]]], [[2, 5, 6, 2, 3], [v = 0, And(-1
< u,u < 0), x = 1, y = u^2-2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [
regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [-7/4, -7/4], [-1/8388608, -1/
8388608]]]], [[2, 5, 6, 2, 4], [v = 0, And(-1 < u,u < 0), x = 1, y = u^2-2, z
= (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [1, 1], [-7/4, -7/4]
, [908093/1048576, 454047/524288]]]], [[2, 5, 6, 2, 5], [v = 0, And(-1 < u,u <
0), x = 1, y = u^2-2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/
2], [1, 1], [-7/4, -7/4], [2, 2]]]], [[2, 9, 4, 2, 1], [v = 0, And(1 < u,u < 2
^(1/2)), x = u^2-1, y = 0, z = z], [regular_chain, [[0, 0], [1265743/1048576,
1265743/1048576], [239655/524288, 479311/1048576], [0, 0], [0, 0]]]], [[3, 13,
6, 2, 1], [0 < v, (v^2+2)^(1/2) < u, x = u^2-v^2-1, y = 0, z = z], [
regular_chain, [[1, 1], [3, 3], [7, 7], [0, 0], [0, 0]]]], [[1, 3, 7, 2, 1], [
v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), 1 < x, y = u^2-v^2-x-1, z =
z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [2, 2], [
-799673/524288, -3198691/2097152], [0, 0]]]], [[1, 7, 4, 5, 1], [v < 0, And(v
< u,u < -v), x = -1, -u^2+v^2 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [0, 0], [-1, -1], [2, 2], [-3, -3]]]], [[1, 7, 4, 5, 2], [v < 0, And
(v < u,u < -v), x = -1, -u^2+v^2 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[-1, -1], [0, 0], [-1, -1], [2, 2], [-1482911/1048576, -741455/524288]]]],
[[1, 7, 4, 5, 3], [v < 0, And(v < u,u < -v), x = -1, -u^2+v^2 < y, And(-(-u^2+
v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0],
[-1, -1], [2, 2], [0, 0]]]], [[1, 7, 4, 5, 4], [v < 0, And(v < u,u < -v), x =
-1, -u^2+v^2 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0],
[-1, -1], [2, 2], [741455/524288, 1482911/1048576]]]], [[1, 7, 4, 5, 5], [v <
0, And(v < u,u < -v), x = -1, -u^2+v^2 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [0, 0], [-1, -1], [2, 2], [3, 3]]]], [[2, 5, 7, 4, 1
], [v = 0, And(-1 < u,u < 0), 1 < x, y = x-u^2+1, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [11/4, 11/4], [-2, -2]]]], [[2,
5, 7, 4, 2], [v = 0, And(-1 < u,u < 0), 1 < x, y = x-u^2+1, z = -(-u^2+1)^(1/2
)], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [11/4, 11/4], [-1816187/
2097152, -3632373/4194304]]]], [[2, 5, 7, 4, 3], [v = 0, And(-1 < u,u < 0), 1
< x, y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain
, [[0, 0], [-1/2, -1/2], [2, 2], [11/4, 11/4], [-1/8388608, -1/8388608]]]], [[
2, 5, 7, 4, 4], [v = 0, And(-1 < u,u < 0), 1 < x, y = x-u^2+1, z = (-u^2+1)^(1
/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [11/4, 11/4], [908093/
1048576, 454047/524288]]]], [[2, 5, 7, 4, 5], [v = 0, And(-1 < u,u < 0), 1 < x
, y = x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [2,
2], [11/4, 11/4], [2, 2]]]], [[2, 9, 5, 2, 1], [v = 0, And(1 < u,u < 2^(1/2)),
And(u^2-1 < x,x < 1), y = u^2-x-1, z = z], [regular_chain, [[0, 0], [1265743/
1048576, 1265743/1048576], [1527887/2097152, 1527887/2097152], [-284633/
1048576, -35579/131072], [0, 0]]]], [[3, 13, 7, 4, 1], [0 < v, (v^2+2)^(1/2) <
u, u^2-v^2-1 < x, y = x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [3, 3], [8
, 8], [1, 1], [0, 0]]]], [[1, 13, 3, 4, 1], [v < 0, (v^2+2)^(1/2) < u, And(-1
< x,x < 1), y = u^2-v^2-x-1, z = z], [regular_chain, [[-1, -1], [3, 3], [0, 0]
, [7, 7], [0, 0]]]], [[2, 4, 1, 2, 1], [v = 0, u = -1, x < -1, y = x, z < 0],
[regular_chain, [[0, 0], [-1, -1], [-2, -2], [-2, -2], [-1, -1]]]], [[2, 4, 1,
2, 2], [v = 0, u = -1, x < -1, y = x, z = 0], [regular_chain, [[0, 0], [-1, -1
], [-2, -2], [-2, -2], [0, 0]]]], [[2, 4, 1, 2, 3], [v = 0, u = -1, x < -1, y
= x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [-2, -2], [-2, -2], [1, 1]]]],
[[3, 4, 4, 1, 1], [0 < v, u = -(v^2+1)^(1/2), x = 0, y < 0, z < 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [0, 0], [-1, -1],
[-1, -1]]]], [[3, 4, 4, 1, 2], [0 < v, u = -(v^2+1)^(1/2), x = 0, y < 0, z = 0
], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [0, 0], [-1, -\
1], [0, 0]]]], [[3, 4, 4, 1, 3], [0 < v, u = -(v^2+1)^(1/2), x = 0, y < 0, 0 <
z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [0, 0], [-1,
-1], [1, 1]]]], [[3, 8, 1, 4, 1], [0 < v, u = v, x < -1, y = -1-x, z < -1], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [1, 1], [-2, -2]]]], [[3, 8, 1, 4, 2
], [0 < v, u = v, x < -1, y = -1-x, z = -1], [regular_chain, [[1, 1], [1, 1],
[-2, -2], [1, 1], [-1, -1]]]], [[3, 8, 1, 4, 3], [0 < v, u = v, x < -1, y = -1
-x, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [1, 1], [-2, -2], [1, 1], [0,
0]]]], [[3, 8, 1, 4, 4], [0 < v, u = v, x < -1, y = -1-x, z = 1], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [1, 1], [1, 1]]]], [[3, 8, 1, 4, 5],
[0 < v, u = v, x < -1, y = -1-x, 1 < z], [regular_chain, [[1, 1], [1, 1], [-2,
-2], [1, 1], [2, 2]]]], [[1, 3, 7, 3, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -
(v^2+1)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [
regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304], [2, 2], [-1/
4194304, -1/4194304], [0, 0]]]], [[1, 7, 5, 1, 1], [v < 0, And(v < u,u < -v),
And(-1 < x,x < 1), y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[-1, -1], [0, 0], [0, 0], [-3, -3], [-3, -3]]]], [[1, 7, 5, 1, 2], [v < 0, 
And(v < u,u < -v), And(-1 < x,x < 1), y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)
], [regular_chain, [[-1, -1], [0, 0], [0, 0], [-3, -3], [-1482911/1048576, -\
741455/524288]]]], [[1, 7, 5, 1, 3], [v < 0, And(v < u,u < -v), And(-1 < x,x <
1), y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [0, 0], [0, 0], [-3, -3], [0, 0]]]], [[1, 7, 5, 1, 4
], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), y < u^2-v^2-x-1, z = (-u^2+v^
2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [-3, -3], [741455/
524288, 1482911/1048576]]]], [[1, 7, 5, 1, 5], [v < 0, And(v < u,u < -v), And(
-1 < x,x < 1), y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1,
-1], [0, 0], [0, 0], [-3, -3], [3, 3]]]], [[2, 5, 7, 3, 1], [v = 0, And(-1 < u
,u < 0), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [0, 0], [-2, -2]]]], [[2, 5, 7,
3, 2], [v = 0, And(-1 < u,u < 0), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), z = -(-
u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [0, 0], [-\
1816187/2097152, -3632373/4194304]]]], [[2, 5, 7, 3, 3], [v = 0, And(-1 < u,u
< 0), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), And(-(-u^2+1)^(1/2) < z,z < (-u^2+1
)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [0, 0], [-1/8388608,
-1/8388608]]]], [[2, 5, 7, 3, 4], [v = 0, And(-1 < u,u < 0), 1 < x, And(u^2-x-\
1 < y,y < x-u^2+1), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2]
, [2, 2], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 5, 7, 3, 5], [v = 0
, And(-1 < u,u < 0), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), (-u^2+1)^(1/2) < z],
[regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [0, 0], [2, 2]]]], [[2, 9, 5, 1
, 1], [v = 0, And(1 < u,u < 2^(1/2)), And(u^2-1 < x,x < 1), y < u^2-x-1, z = z
], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576], [1527887/
2097152, 1527887/2097152], [-2, -2], [0, 0]]]], [[3, 13, 7, 5, 1], [0 < v, (v^
2+2)^(1/2) < u, u^2-v^2-1 < x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[1, 1
], [3, 3], [8, 8], [2, 2], [0, 0]]]], [[1, 13, 3, 5, 1], [v < 0, (v^2+2)^(1/2)
< u, And(-1 < x,x < 1), u^2-v^2-x-1 < y, z = z], [regular_chain, [[-1, -1], [3
, 3], [0, 0], [8, 8], [0, 0]]]], [[2, 4, 1, 3, 1], [v = 0, u = -1, x < -1, And
(x < y,y < -x), z < 0], [regular_chain, [[0, 0], [-1, -1], [-2, -2], [0, 0], [
-1, -1]]]], [[2, 4, 1, 3, 2], [v = 0, u = -1, x < -1, And(x < y,y < -x), z = 0
], [regular_chain, [[0, 0], [-1, -1], [-2, -2], [0, 0], [0, 0]]]], [[2, 4, 1,
3, 3], [v = 0, u = -1, x < -1, And(x < y,y < -x), 0 < z], [regular_chain, [[0,
0], [-1, -1], [-2, -2], [0, 0], [1, 1]]]], [[3, 4, 3, 5, 1], [0 < v, u = -(v^2
+1)^(1/2), And(-1 < x,x < 0), -x < y, z < 0], [regular_chain, [[1, 1], [-\
1482911/1048576, -741455/524288], [-1/2, -1/2], [2, 2], [-1, -1]]]], [[3, 4, 3
, 5, 2], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), -x < y, z = 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [2,
2], [0, 0]]]], [[3, 4, 3, 5, 3], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0)
, -x < y, 0 < z], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288],
[-1/2, -1/2], [2, 2], [1, 1]]]], [[3, 8, 1, 3, 1], [0 < v, u = v, x < -1, And(
x+1 < y,y < -1-x), z < -1], [regular_chain, [[1, 1], [1, 1], [-2, -2], [0, 0],
[-2, -2]]]], [[3, 8, 1, 3, 2], [0 < v, u = v, x < -1, And(x+1 < y,y < -1-x), z
= -1], [regular_chain, [[1, 1], [1, 1], [-2, -2], [0, 0], [-1, -1]]]], [[3, 8,
1, 3, 3], [0 < v, u = v, x < -1, And(x+1 < y,y < -1-x), And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [1, 1], [-2, -2], [0, 0], [0, 0]]]], [[3, 8, 1, 3, 4],
[0 < v, u = v, x < -1, And(x+1 < y,y < -1-x), z = 1], [regular_chain, [[1, 1],
[1, 1], [-2, -2], [0, 0], [1, 1]]]], [[3, 8, 1, 3, 5], [0 < v, u = v, x < -1,
And(x+1 < y,y < -1-x), 1 < z], [regular_chain, [[1, 1], [1, 1], [-2, -2], [0,
0], [2, 2]]]], [[1, 3, 6, 5, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(
1/2)), x = 1, -u^2+v^2+2 < y, z = z], [regular_chain, [[-1, -1], [-6598195/
4194304, -6598195/4194304], [1, 1], [2, 2], [0, 0]]]], [[1, 7, 5, 2, 1], [v <
0, And(v < u,u < -v), And(-1 < x,x < 1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1
/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [-2, -2], [-3, -3]]]], [[1, 7
, 5, 2, 2], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), y = u^2-v^2-x-1, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [-2, -2], [-\
1482911/1048576, -741455/524288]]]], [[1, 7, 5, 2, 3], [v < 0, And(v < u,u < -
v), And(-1 < x,x < 1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+
v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0], [0, 0], [-2, -2], [0, 0]]]]
, [[1, 7, 5, 2, 4], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), y = u^2-v^2-
x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0], [-2,
-2], [741455/524288, 1482911/1048576]]]], [[1, 7, 5, 2, 5], [v < 0, And(v < u,
u < -v), And(-1 < x,x < 1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [0, 0], [0, 0], [-2, -2], [3, 3]]]], [[2, 5, 7, 2, 1
], [v = 0, And(-1 < u,u < 0), 1 < x, y = u^2-x-1, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [-11/4, -11/4], [-2, -2]]]], [[2
, 5, 7, 2, 2], [v = 0, And(-1 < u,u < 0), 1 < x, y = u^2-x-1, z = -(-u^2+1)^(1
/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [-11/4, -11/4], [-1816187
/2097152, -3632373/4194304]]]], [[2, 5, 7, 2, 3], [v = 0, And(-1 < u,u < 0), 1
< x, y = u^2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain
, [[0, 0], [-1/2, -1/2], [2, 2], [-11/4, -11/4], [-1/8388608, -1/8388608]]]],
[[2, 5, 7, 2, 4], [v = 0, And(-1 < u,u < 0), 1 < x, y = u^2-x-1, z = (-u^2+1)^
(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [-11/4, -11/4], [908093
/1048576, 454047/524288]]]], [[2, 5, 7, 2, 5], [v = 0, And(-1 < u,u < 0), 1 <
x, y = u^2-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [-1/2, -1/2], [2
, 2], [-11/4, -11/4], [2, 2]]]], [[2, 9, 5, 4, 1], [v = 0, And(1 < u,u < 2^(1/
2)), And(u^2-1 < x,x < 1), y = x-u^2+1, z = z], [regular_chain, [[0, 0], [
1265743/1048576, 1265743/1048576], [1527887/2097152, 1527887/2097152], [35579/
131072, 284633/1048576], [0, 0]]]], [[3, 13, 7, 2, 1], [0 < v, (v^2+2)^(1/2) <
u, u^2-v^2-1 < x, y = u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [3, 3], [8
, 8], [-1, -1], [0, 0]]]], [[1, 13, 3, 2, 1], [v < 0, (v^2+2)^(1/2) < u, And(-\
1 < x,x < 1), y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [3, 3], [0,
0], [-7, -7], [0, 0]]]], [[2, 4, 1, 4, 1], [v = 0, u = -1, x < -1, y = -x, z <
0], [regular_chain, [[0, 0], [-1, -1], [-2, -2], [2, 2], [-1, -1]]]], [[2, 4,
1, 4, 2], [v = 0, u = -1, x < -1, y = -x, z = 0], [regular_chain, [[0, 0], [-1
, -1], [-2, -2], [2, 2], [0, 0]]]], [[2, 4, 1, 4, 3], [v = 0, u = -1, x < -1,
y = -x, 0 < z], [regular_chain, [[0, 0], [-1, -1], [-2, -2], [2, 2], [1, 1]]]]
, [[3, 4, 3, 4, 1], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y = -x, z <
0], [regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1/2, -1/2],
[1/2, 1/2], [-1, -1]]]], [[3, 4, 3, 4, 2], [0 < v, u = -(v^2+1)^(1/2), And(-1
< x,x < 0), y = -x, z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [-1/2, -1/2], [1/2, 1/2], [0, 0]]]], [[3, 4, 3, 4, 3], [0 < v,
u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y = -x, 0 < z], [regular_chain, [[1, 1]
, [-1482911/1048576, -741455/524288], [-1/2, -1/2], [1/2, 1/2], [1, 1]]]], [[3
, 8, 2, 1, 1], [0 < v, u = v, x = -1, y < 0, z < -1], [regular_chain, [[1, 1],
[1, 1], [-1, -1], [-1, -1], [-2, -2]]]], [[3, 8, 2, 1, 2], [0 < v, u = v, x =
-1, y < 0, z = -1], [regular_chain, [[1, 1], [1, 1], [-1, -1], [-1, -1], [-1,
-1]]]], [[3, 8, 2, 1, 3], [0 < v, u = v, x = -1, y < 0, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [1, 1], [-1, -1], [-1, -1], [0, 0]]]], [[3, 8, 2, 1, 4
], [0 < v, u = v, x = -1, y < 0, z = 1], [regular_chain, [[1, 1], [1, 1], [-1,
-1], [-1, -1], [1, 1]]]], [[3, 8, 2, 1, 5], [0 < v, u = v, x = -1, y < 0, 1 <
z], [regular_chain, [[1, 1], [1, 1], [-1, -1], [-1, -1], [2, 2]]]], [[1, 3, 7,
1, 1], [v < 0, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), 1 < x, y < u^2-v^2-
x-1, z = z], [regular_chain, [[-1, -1], [-6598195/4194304, -6598195/4194304],
[2, 2], [-3, -3], [0, 0]]]], [[1, 7, 5, 3, 1], [v < 0, And(v < u,u < -v), And(
-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [0, 0], [0, 0], [0, 0], [-3, -3]]]], [[1, 7, 5, 3,
2], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^
2+v^2+1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [0, 0], [0, 0],
[0, 0], [-1482911/1048576, -741455/524288]]]], [[1, 7, 5, 3, 3], [v < 0, And(v
< u,u < -v), And(-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u
^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [0, 0
], [0, 0], [0, 0], [0, 0]]]], [[1, 7, 5, 3, 4], [v < 0, And(v < u,u < -v), And
(-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [0, 0], [0, 0], [0, 0], [741455/524288, 1482911/
1048576]]]], [[1, 7, 5, 3, 5], [v < 0, And(v < u,u < -v), And(-1 < x,x < 1), 
And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[-1, -1], [0, 0], [0, 0], [0, 0], [3, 3]]]], [[2, 5, 7, 1, 1], [v = 0, And(-1
< u,u < 0), 1 < x, y < u^2-x-1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0],
[-1/2, -1/2], [2, 2], [-4, -4], [-2, -2]]]], [[2, 5, 7, 1, 2], [v = 0, And(-1
< u,u < 0), 1 < x, y < u^2-x-1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0],
[-1/2, -1/2], [2, 2], [-4, -4], [-1816187/2097152, -3632373/4194304]]]], [[2,
5, 7, 1, 3], [v = 0, And(-1 < u,u < 0), 1 < x, y < u^2-x-1, And(-(-u^2+1)^(1/2
) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [-4
, -4], [-1/8388608, -1/8388608]]]], [[2, 5, 7, 1, 4], [v = 0, And(-1 < u,u < 0
), 1 < x, y < u^2-x-1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1
/2], [2, 2], [-4, -4], [908093/1048576, 454047/524288]]]], [[2, 5, 7, 1, 5], [
v = 0, And(-1 < u,u < 0), 1 < x, y < u^2-x-1, (-u^2+1)^(1/2) < z], [
regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [-4, -4], [2, 2]]]], [[2, 9, 5,
3, 1], [v = 0, And(1 < u,u < 2^(1/2)), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,y
< x-u^2+1), z = z], [regular_chain, [[0, 0], [1265743/1048576, 1265743/1048576
], [1527887/2097152, 1527887/2097152], [0, 0], [0, 0]]]], [[3, 13, 7, 3, 1], [
0 < v, (v^2+2)^(1/2) < u, u^2-v^2-1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1),
z = z], [regular_chain, [[1, 1], [3, 3], [8, 8], [0, 0], [0, 0]]]], [[1, 13, 3
, 3, 1], [v < 0, (v^2+2)^(1/2) < u, And(-1 < x,x < 1), And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z = z], [regular_chain, [[-1, -1], [3, 3], [0, 0], [0, 0], [0, 0
]]]], [[2, 4, 1, 5, 1], [v = 0, u = -1, x < -1, -x < y, z < 0], [regular_chain
, [[0, 0], [-1, -1], [-2, -2], [3, 3], [-1, -1]]]], [[2, 4, 1, 5, 2], [v = 0,
u = -1, x < -1, -x < y, z = 0], [regular_chain, [[0, 0], [-1, -1], [-2, -2], [
3, 3], [0, 0]]]], [[2, 4, 1, 5, 3], [v = 0, u = -1, x < -1, -x < y, 0 < z], [
regular_chain, [[0, 0], [-1, -1], [-2, -2], [3, 3], [1, 1]]]], [[3, 4, 3, 3, 1
], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), And(x < y,y < -x), z < 0], [
regular_chain, [[1, 1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [0,
0], [-1, -1]]]], [[3, 4, 3, 3, 2], [0 < v, u = -(v^2+1)^(1/2), And(-1 < x,x <
0), And(x < y,y < -x), z = 0], [regular_chain, [[1, 1], [-1482911/1048576, -\
741455/524288], [-1/2, -1/2], [0, 0], [0, 0]]]], [[3, 4, 3, 3, 3], [0 < v, u =
-(v^2+1)^(1/2), And(-1 < x,x < 0), And(x < y,y < -x), 0 < z], [regular_chain,
[[1, 1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [0, 0], [1, 1]]]],
[[3, 8, 1, 5, 1], [0 < v, u = v, x < -1, -1-x < y, z < -1], [regular_chain, [[
1, 1], [1, 1], [-2, -2], [2, 2], [-2, -2]]]], [[3, 8, 1, 5, 2], [0 < v, u = v,
x < -1, -1-x < y, z = -1], [regular_chain, [[1, 1], [1, 1], [-2, -2], [2, 2],
[-1, -1]]]], [[3, 8, 1, 5, 3], [0 < v, u = v, x < -1, -1-x < y, And(-1 < z,z <
1)], [regular_chain, [[1, 1], [1, 1], [-2, -2], [2, 2], [0, 0]]]], [[3, 8, 1,
5, 4], [0 < v, u = v, x < -1, -1-x < y, z = 1], [regular_chain, [[1, 1], [1, 1
], [-2, -2], [2, 2], [1, 1]]]], [[3, 8, 1, 5, 5], [0 < v, u = v, x < -1, -1-x
< y, 1 < z], [regular_chain, [[1, 1], [1, 1], [-2, -2], [2, 2], [2, 2]]]], [[1
, 4, 5, 2, 1], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y = -x, z < 0], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [-1/
2, -1/2], [-1, -1]]]], [[1, 4, 5, 2, 2], [v < 0, u = -(v^2+1)^(1/2), And(0 < x
,x < 1), y = -x, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455
/524288], [1/2, 1/2], [-1/2, -1/2], [0, 0]]]], [[1, 4, 5, 2, 3], [v < 0, u = -
(v^2+1)^(1/2), And(0 < x,x < 1), y = -x, 0 < z], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [1/2, 1/2], [-1/2, -1/2], [1, 1]]]], [[1, 9,
5, 3, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And
(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152]
, [-3/8388608, -3/8388608], [-2, -2]]]], [[1, 9, 5, 3, 2], [v < 0, And(-v < u,
u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^
2+1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [479311/2097152, 479311/2097152], [-3/8388608, -3/8388608],
[-772605/1048576, -1545209/2097152]]]], [[1, 9, 5, 3, 3], [v < 0, And(-v < u,u
< (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+
1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1
, -1], [1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [
-3/8388608, -3/8388608], [-1/4194304, -1/4194304]]]], [[1, 9, 5, 3, 4], [v < 0
, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1 < y
,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-3/
8388608, -3/8388608], [193151/262144, 772605/1048576]]]], [[1, 9, 5, 3, 5], [v
< 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1
< y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-3/
8388608, -3/8388608], [2, 2]]]], [[2, 6, 1, 4, 1], [v = 0, u = 0, x < -1, y =
-1-x, z < -1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [1, 1], [-2, -2]]]],
[[2, 6, 1, 4, 2], [v = 0, u = 0, x < -1, y = -1-x, z = -1], [regular_chain, [[
0, 0], [0, 0], [-2, -2], [1, 1], [-1, -1]]]], [[2, 6, 1, 4, 3], [v = 0, u = 0,
x < -1, y = -1-x, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [-2, -2
], [1, 1], [0, 0]]]], [[2, 6, 1, 4, 4], [v = 0, u = 0, x < -1, y = -1-x, z = 1
], [regular_chain, [[0, 0], [0, 0], [-2, -2], [1, 1], [1, 1]]]], [[2, 6, 1, 4,
5], [v = 0, u = 0, x < -1, y = -1-x, 1 < z], [regular_chain, [[0, 0], [0, 0],
[-2, -2], [1, 1], [2, 2]]]], [[2, 11, 1, 5, 1], [v = 0, 2^(1/2) < u, x < -1, u
^2-x-1 < y, z = z], [regular_chain, [[0, 0], [3, 3], [-2, -2], [11, 11], [0, 0
]]]], [[1, 11, 7, 1, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), 1 <
x, y < u^2-v^2-x-1, z = z], [regular_chain, [[-1, -1], [3299097/2097152, 
3299097/2097152], [2, 2], [-3, -3], [0, 0]]]], [[2, 3, 7, 2, 1], [v = 0, And(-
2^(1/2) < u,u < -1), 1 < x, y = u^2-x-1, z = z], [regular_chain, [[0, 0], [-\
1265743/1048576, -1265743/1048576], [2, 2], [-3235683/2097152, -1617841/
1048576], [0, 0]]]], [[3, 2, 3, 3, 1], [0 < v, u = -(v^2+2)^(1/2), And(-1 < x,
x < 1), And(x-1 < y,y < 1-x), z = z], [regular_chain, [[1, 1], [-1816187/
1048576, -3632373/2097152], [0, 0], [0, 0], [0, 0]]]], [[3, 7, 4, 1, 1], [0 <
v, And(-v < u,u < v), x = -1, y < u^2-v^2, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-1, -1], [-2, -2], [-3, -3]]]], [[3, 7, 4, 1,
2], [0 < v, And(-v < u,u < v), x = -1, y < u^2-v^2, z = -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[1, 1], [0, 0], [-1, -1], [-2, -2], [-1482911/1048576, -\
741455/524288]]]], [[3, 7, 4, 1, 3], [0 < v, And(-v < u,u < v), x = -1, y < u^
2-v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [
[1, 1], [0, 0], [-1, -1], [-2, -2], [0, 0]]]], [[3, 7, 4, 1, 4], [0 < v, And(-
v < u,u < v), x = -1, y < u^2-v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [0, 0], [-1, -1], [-2, -2], [741455/524288, 1482911/1048576]]]], [[3, 7
, 4, 1, 5], [0 < v, And(-v < u,u < v), x = -1, y < u^2-v^2, (-u^2+v^2+1)^(1/2)
< z], [regular_chain, [[1, 1], [0, 0], [-1, -1], [-2, -2], [3, 3]]]], [[1, 4,
5, 1, 1], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y < -x, z < 0], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [-2,
-2], [-1, -1]]]], [[1, 4, 5, 1, 2], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x <
1), y < -x, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [1/2, 1/2], [-2, -2], [0, 0]]]], [[1, 4, 5, 1, 3], [v < 0, u = -(v^2+
1)^(1/2), And(0 < x,x < 1), y < -x, 0 < z], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [1/2, 1/2], [-2, -2], [1, 1]]]], [[1, 9, 5,
2, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^
2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [479311/2097152, 479311/2097152], [-808921/1048576,
-3235683/4194304], [-2, -2]]]], [[1, 9, 5, 2, 2], [v < 0, And(-v < u,u < (v^2+
1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/
2097152, 479311/2097152], [-808921/1048576, -3235683/4194304], [-772605/
1048576, -1545209/2097152]]]], [[1, 9, 5, 2, 3], [v < 0, And(-v < u,u < (v^2+1
)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) <
z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [479311/2097152, 479311/2097152], [-808921/1048576, -3235683
/4194304], [-1/4194304, -1/4194304]]]], [[1, 9, 5, 2, 4], [v < 0, And(-v < u,u
< (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)^
(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311
/2097152, 479311/2097152], [-808921/1048576, -3235683/4194304], [193151/262144
, 772605/1048576]]]], [[1, 9, 5, 2, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/2097152,
479311/2097152], [-808921/1048576, -3235683/4194304], [2, 2]]]], [[2, 6, 1, 5,
1], [v = 0, u = 0, x < -1, -1-x < y, z < -1], [regular_chain, [[0, 0], [0, 0],
[-2, -2], [2, 2], [-2, -2]]]], [[2, 6, 1, 5, 2], [v = 0, u = 0, x < -1, -1-x <
y, z = -1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [2, 2], [-1, -1]]]], [[
2, 6, 1, 5, 3], [v = 0, u = 0, x < -1, -1-x < y, And(-1 < z,z < 1)], [
regular_chain, [[0, 0], [0, 0], [-2, -2], [2, 2], [0, 0]]]], [[2, 6, 1, 5, 4],
[v = 0, u = 0, x < -1, -1-x < y, z = 1], [regular_chain, [[0, 0], [0, 0], [-2,
-2], [2, 2], [1, 1]]]], [[2, 6, 1, 5, 5], [v = 0, u = 0, x < -1, -1-x < y, 1 <
z], [regular_chain, [[0, 0], [0, 0], [-2, -2], [2, 2], [2, 2]]]], [[2, 11, 2,
1, 1], [v = 0, 2^(1/2) < u, x = -1, y < -u^2, z = z], [regular_chain, [[0, 0],
[3, 3], [-1, -1], [-10, -10], [0, 0]]]], [[1, 11, 6, 5, 1], [v < 0, And((v^2+1
)^(1/2) < u,u < (v^2+2)^(1/2)), x = 1, -u^2+v^2+2 < y, z = z], [regular_chain,
[[-1, -1], [3299097/2097152, 3299097/2097152], [1, 1], [2, 2], [0, 0]]]], [[2,
3, 7, 1, 1], [v = 0, And(-2^(1/2) < u,u < -1), 1 < x, y < u^2-x-1, z = z], [
regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [2, 2], [-3, -3]
, [0, 0]]]], [[3, 2, 3, 4, 1], [0 < v, u = -(v^2+2)^(1/2), And(-1 < x,x < 1),
y = 1-x, z = z], [regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152]
, [0, 0], [1, 1], [0, 0]]]], [[3, 7, 4, 2, 1], [0 < v, And(-v < u,u < v), x =
-1, y = u^2-v^2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-\
1, -1], [-1, -1], [-3, -3]]]], [[3, 7, 4, 2, 2], [0 < v, And(-v < u,u < v), x
= -1, y = u^2-v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0],
[-1, -1], [-1, -1], [-1482911/1048576, -741455/524288]]]], [[3, 7, 4, 2, 3], [
0 < v, And(-v < u,u < v), x = -1, y = u^2-v^2, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-1, -1], [-1, -1], [0,
0]]]], [[3, 7, 4, 2, 4], [0 < v, And(-v < u,u < v), x = -1, y = u^2-v^2, z = (
-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -1], [-1, -1], [
741455/524288, 1482911/1048576]]]], [[3, 7, 4, 2, 5], [0 < v, And(-v < u,u < v
), x = -1, y = u^2-v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0,
0], [-1, -1], [-1, -1], [3, 3]]]], [[1, 4, 5, 4, 1], [v < 0, u = -(v^2+1)^(1/2
), And(0 < x,x < 1), y = x, z < 0], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [1/2, 1/2], [1/2, 1/2], [-1, -1]]]], [[1, 4, 5, 4, 2
], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y = x, z = 0], [regular_chain
, [[-1, -1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [1/2, 1/2], [0, 0
]]]], [[1, 4, 5, 4, 3], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1), y = x, 0
< z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1/2, 1/2
], [1/2, 1/2], [1, 1]]]], [[1, 9, 5, 1, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/
2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/2097152,
479311/2097152], [-2, -2], [-2, -2]]]], [[1, 9, 5, 1, 2], [v < 0, And(-v < u,u
< (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, z = -(-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [
479311/2097152, 479311/2097152], [-2, -2], [-772605/1048576, -1545209/2097152]
]]], [[1, 9, 5, 1, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 <
x,x < 1), y < u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))
], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/
2097152, 479311/2097152], [-2, -2], [-1/4194304, -1/4194304]]]], [[1, 9, 5, 1,
4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-v
^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576,
1265743/1048576], [479311/2097152, 479311/2097152], [-2, -2], [193151/262144,
772605/1048576]]]], [[1, 9, 5, 1, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), 
And(u^2-v^2-1 < x,x < 1), y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [479311/2097152,
479311/2097152], [-2, -2], [2, 2]]]], [[2, 6, 2, 1, 1], [v = 0, u = 0, x = -1,
y < 0, z < -1], [regular_chain, [[0, 0], [0, 0], [-1, -1], [-1, -1], [-2, -2]]
]], [[2, 6, 2, 1, 2], [v = 0, u = 0, x = -1, y < 0, z = -1], [regular_chain, [
[0, 0], [0, 0], [-1, -1], [-1, -1], [-1, -1]]]], [[2, 6, 2, 1, 3], [v = 0, u =
0, x = -1, y < 0, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [-1, -1
], [-1, -1], [0, 0]]]], [[2, 6, 2, 1, 4], [v = 0, u = 0, x = -1, y < 0, z = 1]
, [regular_chain, [[0, 0], [0, 0], [-1, -1], [-1, -1], [1, 1]]]], [[2, 6, 2, 1
, 5], [v = 0, u = 0, x = -1, y < 0, 1 < z], [regular_chain, [[0, 0], [0, 0], [
-1, -1], [-1, -1], [2, 2]]]], [[2, 11, 1, 3, 1], [v = 0, 2^(1/2) < u, x < -1,
And(x-u^2+1 < y,y < u^2-x-1), z = z], [regular_chain, [[0, 0], [3, 3], [-2, -2
], [0, 0], [0, 0]]]], [[1, 11, 7, 3, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^
2+2)^(1/2)), 1 < x, And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [
regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [2, 2], [0, 0],
[0, 0]]]], [[2, 3, 6, 5, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = 1, -u^2+2 <
y, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [1,
1], [2, 2], [0, 0]]]], [[3, 2, 3, 5, 1], [0 < v, u = -(v^2+2)^(1/2), And(-1 <
x,x < 1), 1-x < y, z = z], [regular_chain, [[1, 1], [-1816187/1048576, -\
3632373/2097152], [0, 0], [2, 2], [0, 0]]]], [[3, 7, 3, 4, 1], [0 < v, And(-v
< u,u < v), And(u^2-v^2-1 < x,x < -1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [1/2, 1/2], [-3, -3]]]], [[
3, 7, 3, 4, 2], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y = x-u^
2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/
2], [1/2, 1/2], [-1482911/1048576, -741455/524288]]]], [[3, 7, 3, 4, 3], [0 <
v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y = x-u^2+v^2+1, And(-(-u^2+v
^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-3
/2, -3/2], [1/2, 1/2], [0, 0]]]], [[3, 7, 3, 4, 4], [0 < v, And(-v < u,u < v),
And(u^2-v^2-1 < x,x < -1), y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [1/2, 1/2], [741455/524288, 
1482911/1048576]]]], [[3, 7, 3, 4, 5], [0 < v, And(-v < u,u < v), And(u^2-v^2-\
1 < x,x < -1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1,
1], [0, 0], [-3/2, -3/2], [1/2, 1/2], [3, 3]]]], [[1, 4, 5, 3, 1], [v < 0, u =
-(v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y < x), z < 0], [regular_chain, [
[-1, -1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [0, 0], [-1, -1]]]],
[[1, 4, 5, 3, 2], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1), And(-x < y,y <
x), z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1/
2, 1/2], [0, 0], [0, 0]]]], [[1, 4, 5, 3, 3], [v < 0, u = -(v^2+1)^(1/2), And(
0 < x,x < 1), And(-x < y,y < x), 0 < z], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [1/2, 1/2], [0, 0], [1, 1]]]], [[1, 9, 4, 3, 1], [v
< 0, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, z < -(-u^2+v^2+1)^(1
/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531
/2097152, -569265/1048576], [1, 1], [-2, -2]]]], [[1, 9, 4, 3, 2], [v < 0, And
(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/
2097152, -569265/1048576], [1, 1], [-772605/1048576, -1545209/2097152]]]], [[1
, 9, 4, 3, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, 
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [1
, 1], [-1/4194304, -1/4194304]]]], [[1, 9, 4, 3, 4], [v < 0, And(-v < u,u < (v
^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/
1048576], [1, 1], [193151/262144, 772605/1048576]]]], [[1, 9, 4, 3, 5], [v < 0
, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, (-u^2+v^2+1)^(1/2) < z]
, [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/
2097152, -569265/1048576], [1, 1], [2, 2]]]], [[2, 6, 2, 2, 1], [v = 0, u = 0,
x = -1, y = 0, z < -1], [regular_chain, [[0, 0], [0, 0], [-1, -1], [0, 0], [-2
, -2]]]], [[2, 6, 2, 2, 2], [v = 0, u = 0, x = -1, y = 0, z = -1], [
regular_chain, [[0, 0], [0, 0], [-1, -1], [0, 0], [-1, -1]]]], [[2, 6, 2, 2, 3
], [v = 0, u = 0, x = -1, y = 0, And(-1 < z,z < 1)], [regular_chain, [[0, 0],
[0, 0], [-1, -1], [0, 0], [0, 0]]]], [[2, 6, 2, 2, 4], [v = 0, u = 0, x = -1,
y = 0, z = 1], [regular_chain, [[0, 0], [0, 0], [-1, -1], [0, 0], [1, 1]]]], [
[2, 6, 2, 2, 5], [v = 0, u = 0, x = -1, y = 0, 1 < z], [regular_chain, [[0, 0]
, [0, 0], [-1, -1], [0, 0], [2, 2]]]], [[2, 11, 1, 4, 1], [v = 0, 2^(1/2) < u,
x < -1, y = u^2-x-1, z = z], [regular_chain, [[0, 0], [3, 3], [-2, -2], [10, 
10], [0, 0]]]], [[1, 11, 7, 2, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(
1/2)), 1 < x, y = u^2-v^2-x-1, z = z], [regular_chain, [[-1, -1], [3299097/
2097152, 3299097/2097152], [2, 2], [-3198693/2097152, -799673/524288], [0, 0]]
]], [[2, 3, 6, 4, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = 1, y = -u^2+2, z =
z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [1, 1], [
569265/1048576, 284633/524288], [0, 0]]]], [[3, 2, 4, 1, 1], [0 < v, u = -(v^2
+2)^(1/2), x = 1, y < 0, z = z], [regular_chain, [[1, 1], [-1816187/1048576, -\
3632373/2097152], [1, 1], [-1, -1], [0, 0]]]], [[3, 7, 3, 5, 1], [0 < v, And(-
v < u,u < v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1 < y, z < -(-u^2+v^2+1)^(1
/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [2, 2], [-3, -3]]]], [[3,
7, 3, 5, 2], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1
< y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2],
[2, 2], [-1482911/1048576, -741455/524288]]]], [[3, 7, 3, 5, 3], [0 < v, And(-
v < u,u < v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1
/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2
], [2, 2], [0, 0]]]], [[3, 7, 3, 5, 4], [0 < v, And(-v < u,u < v), And(u^2-v^2
-1 < x,x < -1), x-u^2+v^2+1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1,
1], [0, 0], [-3/2, -3/2], [2, 2], [741455/524288, 1482911/1048576]]]], [[3, 7,
3, 5, 5], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), x-u^2+v^2+1 <
y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [2,
2], [3, 3]]]], [[1, 11, 7, 5, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1
/2)), 1 < x, x-u^2+v^2+1 < y, z = z], [regular_chain, [[-1, -1], [3299097/
2097152, 3299097/2097152], [2, 2], [3, 3], [0, 0]]]], [[2, 4, 1, 1, 1], [v = 0
, u = -1, x < -1, y < x, z < 0], [regular_chain, [[0, 0], [-1, -1], [-2, -2],
[-3, -3], [-1, -1]]]], [[2, 4, 1, 1, 2], [v = 0, u = -1, x < -1, y < x, z = 0]
, [regular_chain, [[0, 0], [-1, -1], [-2, -2], [-3, -3], [0, 0]]]], [[2, 4, 1,
1, 3], [v = 0, u = -1, x < -1, y < x, 0 < z], [regular_chain, [[0, 0], [-1, -1
], [-2, -2], [-3, -3], [1, 1]]]], [[3, 2, 4, 2, 1], [0 < v, u = -(v^2+2)^(1/2)
, x = 1, y = 0, z = z], [regular_chain, [[1, 1], [-1816187/1048576, -3632373/
2097152], [1, 1], [0, 0], [0, 0]]]], [[3, 7, 4, 5, 1], [0 < v, And(-v < u,u <
v), x = -1, -u^2+v^2 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
0, 0], [-1, -1], [2, 2], [-3, -3]]]], [[3, 7, 4, 5, 2], [0 < v, And(-v < u,u <
v), x = -1, -u^2+v^2 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [
0, 0], [-1, -1], [2, 2], [-1482911/1048576, -741455/524288]]]], [[3, 7, 4, 5,
3], [0 < v, And(-v < u,u < v), x = -1, -u^2+v^2 < y, And(-(-u^2+v^2+1)^(1/2) <
z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-1, -1], [2, 2],
[0, 0]]]], [[3, 7, 4, 5, 4], [0 < v, And(-v < u,u < v), x = -1, -u^2+v^2 < y,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -1], [2, 2], [
741455/524288, 1482911/1048576]]]], [[3, 7, 4, 5, 5], [0 < v, And(-v < u,u < v
), x = -1, -u^2+v^2 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0,
0], [-1, -1], [2, 2], [3, 3]]]], [[1, 4, 4, 1, 1], [v < 0, u = -(v^2+1)^(1/2),
x = 0, y < 0, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [0, 0], [-1, -1], [-1, -1]]]], [[1, 4, 4, 1, 2], [v < 0, u = -(v^2+1)
^(1/2), x = 0, y < 0, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -\
741455/524288], [0, 0], [-1, -1], [0, 0]]]], [[1, 4, 4, 1, 3], [v < 0, u = -(v
^2+1)^(1/2), x = 0, y < 0, 0 < z], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [0, 0], [-1, -1], [1, 1]]]], [[1, 9, 4, 2, 1], [v <
0, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, z < -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/
2097152, -569265/1048576], [0, 0], [-2, -2]]]], [[1, 9, 4, 2, 2], [v < 0, And(
-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/
2097152, -569265/1048576], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[1
, 9, 4, 2, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, 
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [0
, 0], [-1/4194304, -1/4194304]]]], [[1, 9, 4, 2, 4], [v < 0, And(-v < u,u < (v
^2+1)^(1/2)), x = u^2-v^2-1, y = 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/
1048576], [0, 0], [193151/262144, 772605/1048576]]]], [[1, 9, 4, 2, 5], [v < 0
, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, (-u^2+v^2+1)^(1/2) < z]
, [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/
2097152, -569265/1048576], [0, 0], [2, 2]]]], [[2, 5, 7, 5, 1], [v = 0, And(-1
< u,u < 0), 1 < x, x-u^2+1 < y, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0],
[-1/2, -1/2], [2, 2], [4, 4], [-2, -2]]]], [[2, 5, 7, 5, 2], [v = 0, And(-1 <
u,u < 0), 1 < x, x-u^2+1 < y, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [
-1/2, -1/2], [2, 2], [4, 4], [-1816187/2097152, -3632373/4194304]]]], [[2, 5,
7, 5, 3], [v = 0, And(-1 < u,u < 0), 1 < x, x-u^2+1 < y, And(-(-u^2+1)^(1/2) <
z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [-1/2, -1/2], [2, 2], [4, 4],
[-1/8388608, -1/8388608]]]], [[2, 5, 7, 5, 4], [v = 0, And(-1 < u,u < 0), 1 <
x, x-u^2+1 < y, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [-1/2, -1/2], [2
, 2], [4, 4], [908093/1048576, 454047/524288]]]], [[2, 5, 7, 5, 5], [v = 0, 
And(-1 < u,u < 0), 1 < x, x-u^2+1 < y, (-u^2+1)^(1/2) < z], [regular_chain, [[
0, 0], [-1/2, -1/2], [2, 2], [4, 4], [2, 2]]]], [[2, 11, 1, 1, 1], [v = 0, 2^(
1/2) < u, x < -1, y < x-u^2+1, z = z], [regular_chain, [[0, 0], [3, 3], [-2, -\
2], [-11, -11], [0, 0]]]], [[1, 11, 7, 4, 1], [v < 0, And((v^2+1)^(1/2) < u,u
< (v^2+2)^(1/2)), 1 < x, y = x-u^2+v^2+1, z = z], [regular_chain, [[-1, -1], [
3299097/2097152, 3299097/2097152], [2, 2], [799673/524288, 1599347/1048576], [
0, 0]]]], [[2, 3, 7, 5, 1], [v = 0, And(-2^(1/2) < u,u < -1), 1 < x, x-u^2+1 <
y, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [2,
2], [3, 3], [0, 0]]]], [[3, 2, 4, 3, 1], [0 < v, u = -(v^2+2)^(1/2), x = 1, 0
< y, z = z], [regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152], [1
, 1], [1, 1], [0, 0]]]], [[3, 7, 5, 1, 1], [0 < v, And(-v < u,u < v), And(-1 <
x,x < 1), y < u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1],
[0, 0], [0, 0], [-3, -3], [-3, -3]]]], [[3, 7, 5, 1, 2], [0 < v, And(-v < u,u
< v), And(-1 < x,x < 1), y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [0, 0], [-3, -3], [-1482911/1048576, -741455/
524288]]]], [[3, 7, 5, 1, 3], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y
< u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [0, 0], [-3, -3], [0, 0]]]], [[3, 7, 5, 1, 4],
[0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y < u^2-v^2-x-1, z = (-u^2+v^2+1
)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [-3, -3], [741455/524288, 
1482911/1048576]]]], [[3, 7, 5, 1, 5], [0 < v, And(-v < u,u < v), And(-1 < x,x
< 1), y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0
], [0, 0], [-3, -3], [3, 3]]]], [[1, 4, 3, 5, 1], [v < 0, u = -(v^2+1)^(1/2),
And(-1 < x,x < 0), -x < y, z < 0], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [-1/2, -1/2], [2, 2], [-1, -1]]]], [[1, 4, 3, 5, 2],
[v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), -x < y, z = 0], [regular_chain,
[[-1, -1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [2, 2], [0, 0]]]]
, [[1, 4, 3, 5, 3], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), -x < y, 0 <
z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1/2, -1/2
], [2, 2], [1, 1]]]], [[1, 9, 4, 1, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x = u^2-v^2-1, y < 0, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [-1, -\
1], [-2, -2]]]], [[1, 9, 4, 1, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x =
u^2-v^2-1, y < 0, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [-1, -\
1], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 4, 1, 3], [v < 0, And(-v <
u,u < (v^2+1)^(1/2)), x = u^2-v^2-1, y < 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-
u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-1138531/2097152, -569265/1048576], [-1, -1], [-1/4194304, -1/
4194304]]]], [[1, 9, 4, 1, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = u^2-
v^2-1, y < 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [-1138531/2097152, -569265/1048576], [-1, -1], [
193151/262144, 772605/1048576]]]], [[1, 9, 4, 1, 5], [v < 0, And(-v < u,u < (v
^2+1)^(1/2)), x = u^2-v^2-1, y < 0, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [-1138531/2097152, -569265/
1048576], [-1, -1], [2, 2]]]], [[2, 6, 1, 1, 1], [v = 0, u = 0, x < -1, y < x+
1, z < -1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [-2, -2], [-2, -2]]]],
[[2, 6, 1, 1, 2], [v = 0, u = 0, x < -1, y < x+1, z = -1], [regular_chain, [[0
, 0], [0, 0], [-2, -2], [-2, -2], [-1, -1]]]], [[2, 6, 1, 1, 3], [v = 0, u = 0
, x < -1, y < x+1, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [-2, -\
2], [-2, -2], [0, 0]]]], [[2, 6, 1, 1, 4], [v = 0, u = 0, x < -1, y < x+1, z =
1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [-2, -2], [1, 1]]]], [[2, 6, 1,
1, 5], [v = 0, u = 0, x < -1, y < x+1, 1 < z], [regular_chain, [[0, 0], [0, 0]
, [-2, -2], [-2, -2], [2, 2]]]], [[2, 11, 1, 2, 1], [v = 0, 2^(1/2) < u, x < -\
1, y = x-u^2+1, z = z], [regular_chain, [[0, 0], [3, 3], [-2, -2], [-10, -10],
[0, 0]]]], [[1, 12, 1, 2, 1], [v < 0, u = (v^2+2)^(1/2), x < -1, y = x-1, z =
z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [-2, -2], [-3
, -3], [0, 0]]]], [[2, 3, 7, 4, 1], [v = 0, And(-2^(1/2) < u,u < -1), 1 < x, y
= x-u^2+1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/
1048576], [2, 2], [1617841/1048576, 808921/524288], [0, 0]]]], [[3, 2, 5, 1, 1
], [0 < v, u = -(v^2+2)^(1/2), 1 < x, y < 1-x, z = z], [regular_chain, [[1, 1]
, [-1816187/1048576, -3632373/2097152], [2, 2], [-2, -2], [0, 0]]]], [[3, 7, 4
, 3, 1], [0 < v, And(-v < u,u < v), x = -1, And(u^2-v^2 < y,y < -u^2+v^2), z <
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -1], [0, 0], [-3,
-3]]]], [[3, 7, 4, 3, 2], [0 < v, And(-v < u,u < v), x = -1, And(u^2-v^2 < y,y
< -u^2+v^2), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -\
1], [0, 0], [-1482911/1048576, -741455/524288]]]], [[3, 7, 4, 3, 3], [0 < v, 
And(-v < u,u < v), x = -1, And(u^2-v^2 < y,y < -u^2+v^2), And(-(-u^2+v^2+1)^(1
/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-1, -1], [
0, 0], [0, 0]]]], [[3, 7, 4, 3, 4], [0 < v, And(-v < u,u < v), x = -1, And(u^2
-v^2 < y,y < -u^2+v^2), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0,
0], [-1, -1], [0, 0], [741455/524288, 1482911/1048576]]]], [[3, 7, 4, 3, 5], [
0 < v, And(-v < u,u < v), x = -1, And(u^2-v^2 < y,y < -u^2+v^2), (-u^2+v^2+1)^
(1/2) < z], [regular_chain, [[1, 1], [0, 0], [-1, -1], [0, 0], [3, 3]]]], [[1,
4, 4, 3, 1], [v < 0, u = -(v^2+1)^(1/2), x = 0, 0 < y, z < 0], [regular_chain,
[[-1, -1], [-1482911/1048576, -741455/524288], [0, 0], [1, 1], [-1, -1]]]], [[
1, 4, 4, 3, 2], [v < 0, u = -(v^2+1)^(1/2), x = 0, 0 < y, z = 0], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [0, 0], [1, 1],
[0, 0]]]], [[1, 4, 4, 3, 3], [v < 0, u = -(v^2+1)^(1/2), x = 0, 0 < y, 0 < z],
[regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [0, 0], [1, 1],
[1, 1]]]], [[1, 9, 3, 5, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x
,x < u^2-v^2-1), u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/
4194304], [2, 2], [-2, -2]]]], [[1, 9, 3, 5, 2], [v < 0, And(-v < u,u < (v^2+1
)^(1/2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [-772605/1048576, -1545209/2097152]]]], [[
1, 9, 3, 5, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-\
1), u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [-1/4194304, -1/4194304]]]], [[1, 9, 3, 5,
4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-
x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576,
1265743/1048576], [-3235683/4194304, -3235683/4194304], [2, 2], [193151/262144
, 772605/1048576]]]], [[1, 9, 3, 5, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [2, 2], [2, 2]]]], [[2, 6, 1, 2, 1], [v = 0, u = 0
, x < -1, y = x+1, z < -1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [-1, -1
], [-2, -2]]]], [[2, 6, 1, 2, 2], [v = 0, u = 0, x < -1, y = x+1, z = -1], [
regular_chain, [[0, 0], [0, 0], [-2, -2], [-1, -1], [-1, -1]]]], [[2, 6, 1, 2,
3], [v = 0, u = 0, x < -1, y = x+1, And(-1 < z,z < 1)], [regular_chain, [[0, 0
], [0, 0], [-2, -2], [-1, -1], [0, 0]]]], [[2, 6, 1, 2, 4], [v = 0, u = 0, x <
-1, y = x+1, z = 1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [-1, -1], [1,
1]]]], [[2, 6, 1, 2, 5], [v = 0, u = 0, x < -1, y = x+1, 1 < z], [
regular_chain, [[0, 0], [0, 0], [-2, -2], [-1, -1], [2, 2]]]], [[2, 10, 5, 4,
1], [v = 0, u = 2^(1/2), 1 < x, y = x-1, z = z], [regular_chain, [[0, 0], [
741455/524288, 1482911/1048576], [2, 2], [1, 1], [0, 0]]]], [[1, 12, 1, 1, 1],
[v < 0, u = (v^2+2)^(1/2), x < -1, y < x-1, z = z], [regular_chain, [[-1, -1],
[908093/524288, 1816187/1048576], [-2, -2], [-4, -4], [0, 0]]]], [[2, 3, 7, 3,
1], [v = 0, And(-2^(1/2) < u,u < -1), 1 < x, And(u^2-x-1 < y,y < x-u^2+1), z =
z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [2, 2], [0,
0], [0, 0]]]], [[3, 2, 5, 2, 1], [0 < v, u = -(v^2+2)^(1/2), 1 < x, y = 1-x, z
= z], [regular_chain, [[1, 1], [-1816187/1048576, -3632373/2097152], [2, 2], [
-1, -1], [0, 0]]]], [[3, 7, 4, 4, 1], [0 < v, And(-v < u,u < v), x = -1, y = -
u^2+v^2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -1],
[1, 1], [-3, -3]]]], [[3, 7, 4, 4, 2], [0 < v, And(-v < u,u < v), x = -1, y =
-u^2+v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -1],
[1, 1], [-1482911/1048576, -741455/524288]]]], [[3, 7, 4, 4, 3], [0 < v, And(-
v < u,u < v), x = -1, y = -u^2+v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+
1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-1, -1], [1, 1], [0, 0]]]], [[3,
7, 4, 4, 4], [0 < v, And(-v < u,u < v), x = -1, y = -u^2+v^2, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[1, 1], [0, 0], [-1, -1], [1, 1], [741455/524288, 
1482911/1048576]]]], [[3, 7, 4, 4, 5], [0 < v, And(-v < u,u < v), x = -1, y =
-u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [-1, -1],
[1, 1], [3, 3]]]], [[1, 4, 4, 2, 1], [v < 0, u = -(v^2+1)^(1/2), x = 0, y = 0,
z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [0, 0],
[0, 0], [-1, -1]]]], [[1, 4, 4, 2, 2], [v < 0, u = -(v^2+1)^(1/2), x = 0, y =
0, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [0,
0], [0, 0], [0, 0]]]], [[1, 4, 4, 2, 3], [v < 0, u = -(v^2+1)^(1/2), x = 0, y
= 0, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [0
, 0], [0, 0], [1, 1]]]], [[1, 9, 3, 4, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2
)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [239655/1048576, 29957/131072], [-2, -2]]]], [[1,
9, 3, 4, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1),
y = u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743
/1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [239655/
1048576, 29957/131072], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 3, 4,
3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-
v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain,
[[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/
4194304], [239655/1048576, 29957/131072], [-1/4194304, -1/4194304]]]], [[1, 9,
3, 4, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y
= u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [239655/
1048576, 29957/131072], [193151/262144, 772605/1048576]]]], [[1, 9, 3, 4, 5],
[v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-
x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [-3235683/4194304, -3235683/4194304], [239655/1048576, 29957
/131072], [2, 2]]]], [[2, 6, 1, 3, 1], [v = 0, u = 0, x < -1, And(x+1 < y,y <
-1-x), z < -1], [regular_chain, [[0, 0], [0, 0], [-2, -2], [0, 0], [-2, -2]]]]
, [[2, 6, 1, 3, 2], [v = 0, u = 0, x < -1, And(x+1 < y,y < -1-x), z = -1], [
regular_chain, [[0, 0], [0, 0], [-2, -2], [0, 0], [-1, -1]]]], [[2, 6, 1, 3, 3
], [v = 0, u = 0, x < -1, And(x+1 < y,y < -1-x), And(-1 < z,z < 1)], [
regular_chain, [[0, 0], [0, 0], [-2, -2], [0, 0], [0, 0]]]], [[2, 6, 1, 3, 4],
[v = 0, u = 0, x < -1, And(x+1 < y,y < -1-x), z = 1], [regular_chain, [[0, 0],
[0, 0], [-2, -2], [0, 0], [1, 1]]]], [[2, 6, 1, 3, 5], [v = 0, u = 0, x < -1,
And(x+1 < y,y < -1-x), 1 < z], [regular_chain, [[0, 0], [0, 0], [-2, -2], [0,
0], [2, 2]]]], [[2, 10, 5, 5, 1], [v = 0, u = 2^(1/2), 1 < x, x-1 < y, z = z],
[regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [2, 2], [2, 2], [0,
0]]]], [[1, 4, 3, 1, 1], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y < x,
z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1/2,
-1/2], [-2, -2], [-1, -1]]]], [[1, 4, 3, 1, 2], [v < 0, u = -(v^2+1)^(1/2), 
And(-1 < x,x < 0), y < x, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576
, -741455/524288], [-1/2, -1/2], [-2, -2], [0, 0]]]], [[1, 4, 3, 1, 3], [v < 0
, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y < x, 0 < z], [regular_chain, [[-1,
-1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [-2, -2], [1, 1]]]], [[
1, 9, 3, 2, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-\
1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [-\
29957/131072, -239655/1048576], [-2, -2]]]], [[1, 9, 3, 2, 2], [v < 0, And(-v
< u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, z = -(-u^2
+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576],
[-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [-\
772605/1048576, -1545209/2097152]]]], [[1, 9, 3, 2, 3], [v < 0, And(-v < u,u <
(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^
(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [-29957/
131072, -239655/1048576], [-1/4194304, -1/4194304]]]], [[1, 9, 3, 2, 4], [v <
0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/
1048576], [193151/262144, 772605/1048576]]]], [[1, 9, 3, 2, 5], [v < 0, And(-v
< u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = x-u^2+v^2+1, (-u^2+v^2+
1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576],
[-3235683/4194304, -3235683/4194304], [-29957/131072, -239655/1048576], [2, 2]
]]], [[2, 6, 3, 5, 1], [v = 0, u = 0, And(-1 < x,x < 1), x+1 < y, z < -1], [
regular_chain, [[0, 0], [0, 0], [0, 0], [2, 2], [-2, -2]]]], [[2, 6, 3, 5, 2],
[v = 0, u = 0, And(-1 < x,x < 1), x+1 < y, z = -1], [regular_chain, [[0, 0], [
0, 0], [0, 0], [2, 2], [-1, -1]]]], [[2, 6, 3, 5, 3], [v = 0, u = 0, And(-1 <
x,x < 1), x+1 < y, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [0, 0]
, [2, 2], [0, 0]]]], [[2, 6, 3, 5, 4], [v = 0, u = 0, And(-1 < x,x < 1), x+1 <
y, z = 1], [regular_chain, [[0, 0], [0, 0], [0, 0], [2, 2], [1, 1]]]], [[2, 6,
3, 5, 5], [v = 0, u = 0, And(-1 < x,x < 1), x+1 < y, 1 < z], [regular_chain, [
[0, 0], [0, 0], [0, 0], [2, 2], [2, 2]]]], [[2, 11, 3, 4, 1], [v = 0, 2^(1/2)
< u, And(-1 < x,x < 1), y = u^2-x-1, z = z], [regular_chain, [[0, 0], [3, 3],
[0, 0], [8, 8], [0, 0]]]], [[1, 11, 5, 2, 1], [v < 0, And((v^2+1)^(1/2) < u,u
< (v^2+2)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = u^2-v^2-x-1, z = z], [
regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [773191/1048576,
773191/1048576], [-137693/524288, -275385/1048576], [0, 0]]]], [[2, 3, 5, 3, 1
], [v = 0, And(-2^(1/2) < u,u < -1), And(u^2-1 < x,x < 1), And(u^2-x-1 < y,y <
x-u^2+1), z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576
], [1527887/2097152, 1527887/2097152], [0, 0], [0, 0]]]], [[3, 2, 5, 4, 1], [0
< v, u = -(v^2+2)^(1/2), 1 < x, y = x-1, z = z], [regular_chain, [[1, 1], [-\
1816187/1048576, -3632373/2097152], [2, 2], [1, 1], [0, 0]]]], [[3, 7, 5, 5, 1
], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), x-u^2+v^2+1 < y, z < -(-u^2+v
^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [3, 3], [-3, -3]]]], [[
3, 7, 5, 5, 2], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), x-u^2+v^2+1 < y,
z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [3, 3], [-\
1482911/1048576, -741455/524288]]]], [[3, 7, 5, 5, 3], [0 < v, And(-v < u,u <
v), And(-1 < x,x < 1), x-u^2+v^2+1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+
v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [0, 0], [3, 3], [0, 0]]]], [[
3, 7, 5, 5, 4], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), x-u^2+v^2+1 < y,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [3, 3], [
741455/524288, 1482911/1048576]]]], [[3, 7, 5, 5, 5], [0 < v, And(-v < u,u < v
), And(-1 < x,x < 1), x-u^2+v^2+1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain
, [[1, 1], [0, 0], [0, 0], [3, 3], [3, 3]]]], [[1, 4, 3, 2, 1], [v < 0, u = -(
v^2+1)^(1/2), And(-1 < x,x < 0), y = x, z < 0], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [-1/2, -1/2], [-1/2, -1/2], [-1, -1]]]], [[1
, 4, 3, 2, 2], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y = x, z = 0], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [-\
1/2, -1/2], [0, 0]]]], [[1, 4, 3, 2, 3], [v < 0, u = -(v^2+1)^(1/2), And(-1 <
x,x < 0), y = x, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455
/524288], [-1/2, -1/2], [-1/2, -1/2], [1, 1]]]], [[1, 9, 3, 3, 1], [v < 0, And
(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [-3235683/4194304, -3235683/4194304], [0, 0], [-2,
-2]]]], [[1, 9, 3, 3, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x
< u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [0, 0], [-772605/1048576, -1545209/2097152]]]], [[
1, 9, 3, 3, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-\
1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^
2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576
], [-3235683/4194304, -3235683/4194304], [0, 0], [-1/4194304, -1/4194304]]]],
[[1, 9, 3, 3, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^
2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [0, 0], [193151/262144, 772605/1048576]]]], [[1, 9
, 3, 3, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1),
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/
4194304], [0, 0], [2, 2]]]], [[2, 6, 3, 4, 1], [v = 0, u = 0, And(-1 < x,x < 1
), y = x+1, z < -1], [regular_chain, [[0, 0], [0, 0], [0, 0], [1, 1], [-2, -2]
]]], [[2, 6, 3, 4, 2], [v = 0, u = 0, And(-1 < x,x < 1), y = x+1, z = -1], [
regular_chain, [[0, 0], [0, 0], [0, 0], [1, 1], [-1, -1]]]], [[2, 6, 3, 4, 3],
[v = 0, u = 0, And(-1 < x,x < 1), y = x+1, And(-1 < z,z < 1)], [regular_chain,
[[0, 0], [0, 0], [0, 0], [1, 1], [0, 0]]]], [[2, 6, 3, 4, 4], [v = 0, u = 0, 
And(-1 < x,x < 1), y = x+1, z = 1], [regular_chain, [[0, 0], [0, 0], [0, 0], [
1, 1], [1, 1]]]], [[2, 6, 3, 4, 5], [v = 0, u = 0, And(-1 < x,x < 1), y = x+1,
1 < z], [regular_chain, [[0, 0], [0, 0], [0, 0], [1, 1], [2, 2]]]], [[2, 11, 3
, 3, 1], [v = 0, 2^(1/2) < u, And(-1 < x,x < 1), And(x-u^2+1 < y,y < u^2-x-1),
z = z], [regular_chain, [[0, 0], [3, 3], [0, 0], [0, 0], [0, 0]]]], [[1, 11, 5
, 3, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(u^2-v^2-1 < x,x
< 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = z], [regular_chain, [[-1, -1],
[3299097/2097152, 3299097/2097152], [773191/1048576, 773191/1048576], [0, 0],
[0, 0]]]], [[2, 3, 5, 4, 1], [v = 0, And(-2^(1/2) < u,u < -1), And(u^2-1 < x,x
< 1), y = x-u^2+1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -\
1265743/1048576], [1527887/2097152, 1527887/2097152], [35579/131072, 284633/
1048576], [0, 0]]]], [[3, 2, 5, 3, 1], [0 < v, u = -(v^2+2)^(1/2), 1 < x, And(
1-x < y,y < x-1), z = z], [regular_chain, [[1, 1], [-1816187/1048576, -3632373
/2097152], [2, 2], [0, 0], [0, 0]]]], [[3, 7, 5, 4, 1], [0 < v, And(-v < u,u <
v), And(-1 < x,x < 1), y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [0, 0], [2, 2], [-3, -3]]]], [[3, 7, 5, 4, 2],
[0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y = x-u^2+v^2+1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [2, 2], [-1482911/1048576,
-741455/524288]]]], [[3, 7, 5, 4, 3], [0 < v, And(-v < u,u < v), And(-1 < x,x
< 1), y = x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [0, 0], [2, 2], [0, 0]]]], [[3, 7, 5, 4, 4], [
0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y = x-u^2+v^2+1, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [2, 2], [741455/524288, 
1482911/1048576]]]], [[3, 7, 5, 4, 5], [0 < v, And(-v < u,u < v), And(-1 < x,x
< 1), y = x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0
], [0, 0], [2, 2], [3, 3]]]], [[1, 4, 3, 3, 1], [v < 0, u = -(v^2+1)^(1/2), 
And(-1 < x,x < 0), And(x < y,y < -x), z < 0], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [-1/2, -1/2], [0, 0], [-1, -1]]]], [[1, 4, 3
, 3, 2], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), And(x < y,y < -x), z =
0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1/2, -1/2
], [0, 0], [0, 0]]]], [[1, 4, 3, 3, 3], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x
,x < 0), And(x < y,y < -x), 0 < z], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [-1/2, -1/2], [0, 0], [1, 1]]]], [[1, 9, 2, 5, 1], [
v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, u^2-v^2 < y, z < -(-u^2+v^2+1)^(
1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1]
, [2, 2], [-2, -2]]]], [[1, 9, 2, 5, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2))
, x = -1, u^2-v^2 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1, -1], [2, 2], [-772605/1048576, -\
1545209/2097152]]]], [[1, 9, 2, 5, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x = -1, u^2-v^2 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1], [2, 2]
, [-1/4194304, -1/4194304]]]], [[1, 9, 2, 5, 4], [v < 0, And(-v < u,u < (v^2+1
)^(1/2)), x = -1, u^2-v^2 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [1265743/1048576, 1265743/1048576], [-1, -1], [2, 2], [193151/262144, 
772605/1048576]]]], [[1, 9, 2, 5, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x
= -1, u^2-v^2 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1, -1], [2, 2], [2, 2]]]], [[2, 6, 4, 2,
1], [v = 0, u = 0, x = 1, y = -2, z < -1], [regular_chain, [[0, 0], [0, 0], [1
, 1], [-2, -2], [-2, -2]]]], [[2, 6, 4, 2, 2], [v = 0, u = 0, x = 1, y = -2, z
= -1], [regular_chain, [[0, 0], [0, 0], [1, 1], [-2, -2], [-1, -1]]]], [[2, 6,
4, 2, 3], [v = 0, u = 0, x = 1, y = -2, And(-1 < z,z < 1)], [regular_chain, [[
0, 0], [0, 0], [1, 1], [-2, -2], [0, 0]]]], [[2, 6, 4, 2, 4], [v = 0, u = 0, x
= 1, y = -2, z = 1], [regular_chain, [[0, 0], [0, 0], [1, 1], [-2, -2], [1, 1]
]]], [[2, 6, 4, 2, 5], [v = 0, u = 0, x = 1, y = -2, 1 < z], [regular_chain, [
[0, 0], [0, 0], [1, 1], [-2, -2], [2, 2]]]], [[2, 11, 3, 2, 1], [v = 0, 2^(1/2
) < u, And(-1 < x,x < 1), y = x-u^2+1, z = z], [regular_chain, [[0, 0], [3, 3]
, [0, 0], [-8, -8], [0, 0]]]], [[1, 11, 5, 4, 1], [v < 0, And((v^2+1)^(1/2) <
u,u < (v^2+2)^(1/2)), And(u^2-v^2-1 < x,x < 1), y = x-u^2+v^2+1, z = z], [
regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [773191/1048576,
773191/1048576], [275385/1048576, 137693/524288], [0, 0]]]], [[2, 3, 5, 1, 1],
[v = 0, And(-2^(1/2) < u,u < -1), And(u^2-1 < x,x < 1), y < u^2-x-1, z = z], [
regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [1527887/2097152
, 1527887/2097152], [-2, -2], [0, 0]]]], [[3, 3, 1, 1, 1], [0 < v, And(-(v^2+2
)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-2, -2], [-4, -\
4], [0, 0]]]], [[3, 7, 5, 3, 1], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1),
And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [0, 0], [0, 0], [0, 0], [-3, -3]]]], [[3, 7, 5, 3, 2], [0 < v, And(
-v < u,u < v), And(-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(
-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [0, 0], [-1482911
/1048576, -741455/524288]]]], [[3, 7, 5, 3, 3], [0 < v, And(-v < u,u < v), And
(-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [0, 0], [0, 0],
[0, 0]]]], [[3, 7, 5, 3, 4], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), And
(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [0, 0], [0, 0], [0, 0], [741455/524288, 1482911/1048576]]]], [[3, 7, 5,
3, 5], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), And(u^2-v^2-x-1 < y,y < x
-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [0, 0],
[0, 0], [3, 3]]]], [[1, 4, 3, 4, 1], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x
< 0), y = -x, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [-1/2, -1/2], [1/2, 1/2], [-1, -1]]]], [[1, 4, 3, 4, 2], [v < 0, u =
-(v^2+1)^(1/2), And(-1 < x,x < 0), y = -x, z = 0], [regular_chain, [[-1, -1],
[-1482911/1048576, -741455/524288], [-1/2, -1/2], [1/2, 1/2], [0, 0]]]], [[1,
4, 3, 4, 3], [v < 0, u = -(v^2+1)^(1/2), And(-1 < x,x < 0), y = -x, 0 < z], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1/2, -1/2], [1
/2, 1/2], [1, 1]]]], [[1, 9, 3, 1, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/
4194304, -3235683/4194304], [-2, -2], [-2, -2]]]], [[1, 9, 3, 1, 2], [v < 0, 
And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, z =
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-772605/1048576, -\
1545209/2097152]]]], [[1, 9, 3, 1, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-
u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [-1/4194304, -1/
4194304]]]], [[1, 9, 3, 1, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 <
x,x < u^2-v^2-1), y < x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[
-1, -1], [1265743/1048576, 1265743/1048576], [-3235683/4194304, -3235683/
4194304], [-2, -2], [193151/262144, 772605/1048576]]]], [[1, 9, 3, 1, 5], [v <
0, And(-v < u,u < (v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y < x-u^2+v^2+1,
(-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-3235683/4194304, -3235683/4194304], [-2, -2], [2, 2]]]], [[2, 6, 4
, 1, 1], [v = 0, u = 0, x = 1, y < -2, z < -1], [regular_chain, [[0, 0], [0, 0
], [1, 1], [-3, -3], [-2, -2]]]], [[2, 6, 4, 1, 2], [v = 0, u = 0, x = 1, y <
-2, z = -1], [regular_chain, [[0, 0], [0, 0], [1, 1], [-3, -3], [-1, -1]]]], [
[2, 6, 4, 1, 3], [v = 0, u = 0, x = 1, y < -2, And(-1 < z,z < 1)], [
regular_chain, [[0, 0], [0, 0], [1, 1], [-3, -3], [0, 0]]]], [[2, 6, 4, 1, 4],
[v = 0, u = 0, x = 1, y < -2, z = 1], [regular_chain, [[0, 0], [0, 0], [1, 1],
[-3, -3], [1, 1]]]], [[2, 6, 4, 1, 5], [v = 0, u = 0, x = 1, y < -2, 1 < z], [
regular_chain, [[0, 0], [0, 0], [1, 1], [-3, -3], [2, 2]]]], [[2, 11, 3, 1, 1]
, [v = 0, 2^(1/2) < u, And(-1 < x,x < 1), y < x-u^2+1, z = z], [regular_chain,
[[0, 0], [3, 3], [0, 0], [-9, -9], [0, 0]]]], [[1, 11, 5, 5, 1], [v < 0, And((
v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), And(u^2-v^2-1 < x,x < 1), x-u^2+v^2+1 < y
, z = z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [
773191/1048576, 773191/1048576], [2, 2], [0, 0]]]], [[2, 3, 5, 2, 1], [v = 0,
And(-2^(1/2) < u,u < -1), And(u^2-1 < x,x < 1), y = u^2-x-1, z = z], [
regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [1527887/2097152
, 1527887/2097152], [-284633/1048576, -35579/131072], [0, 0]]]], [[3, 2, 5, 5,
1], [0 < v, u = -(v^2+2)^(1/2), 1 < x, x-1 < y, z = z], [regular_chain, [[1, 1
], [-1816187/1048576, -3632373/2097152], [2, 2], [2, 2], [0, 0]]]], [[3, 7, 5,
2, 1], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y = u^2-v^2-x-1, z < -(-u
^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [-2, -2], [-3, -3]]
]], [[3, 7, 5, 2, 2], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y = u^2-v^
2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [-2,
-2], [-1482911/1048576, -741455/524288]]]], [[3, 7, 5, 2, 3], [0 < v, And(-v <
u,u < v), And(-1 < x,x < 1), y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z <
(-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [0, 0], [-2, -2], [0, 0
]]]], [[3, 7, 5, 2, 4], [0 < v, And(-v < u,u < v), And(-1 < x,x < 1), y = u^2-
v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [0, 0], [-2
, -2], [741455/524288, 1482911/1048576]]]], [[3, 7, 5, 2, 5], [0 < v, And(-v <
u,u < v), And(-1 < x,x < 1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [0, 0], [0, 0], [-2, -2], [3, 3]]]], [[1, 11, 6, 1, 1]
, [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = 1, y < u^2-v^2-2, z =
z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [1, 1], [-2
, -2], [0, 0]]]], [[2, 3, 6, 2, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = 1, y
= u^2-2, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576]
, [1, 1], [-1138531/2097152, -569265/1048576], [0, 0]]]], [[3, 3, 1, 3, 1], [0
< v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, And(x-u^2+v^2+1 < y,y
< u^2-v^2-x-1), z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/
4194304], [-2, -2], [0, 0], [0, 0]]]], [[3, 7, 6, 4, 1], [0 < v, And(-v < u,u
< v), x = 1, y = -u^2+v^2+2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [0, 0], [1, 1], [3, 3], [-3, -3]]]], [[3, 7, 6, 4, 2], [0 < v, And(-v < u,u
< v), x = 1, y = -u^2+v^2+2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [0, 0], [1, 1], [3, 3], [-1482911/1048576, -741455/524288]]]], [[3, 7, 6, 4,
3], [0 < v, And(-v < u,u < v), x = 1, y = -u^2+v^2+2, And(-(-u^2+v^2+1)^(1/2)
< z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [1, 1], [3, 3],
[0, 0]]]], [[3, 7, 6, 4, 4], [0 < v, And(-v < u,u < v), x = 1, y = -u^2+v^2+2,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [1, 1], [3, 3], [
741455/524288, 1482911/1048576]]]], [[3, 7, 6, 4, 5], [0 < v, And(-v < u,u < v
), x = 1, y = -u^2+v^2+2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0
, 0], [1, 1], [3, 3], [3, 3]]]], [[1, 4, 2, 2, 1], [v < 0, u = -(v^2+1)^(1/2),
x = -1, y = -1, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [-1, -1], [-1, -1], [-1, -1]]]], [[1, 4, 2, 2, 2], [v < 0, u = -(v^2+
1)^(1/2), x = -1, y = -1, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576
, -741455/524288], [-1, -1], [-1, -1], [0, 0]]]], [[1, 4, 2, 2, 3], [v < 0, u
= -(v^2+1)^(1/2), x = -1, y = -1, 0 < z], [regular_chain, [[-1, -1], [-1482911
/1048576, -741455/524288], [-1, -1], [-1, -1], [1, 1]]]], [[1, 9, 2, 3, 1], [v
< 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z <
-(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-1, -1], [0, 0], [-2, -2]]]], [[1, 9, 2, 3, 2], [v < 0, And(-v < u,
u < (v^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), z = -(-u^2+v^2+1)^(
1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1]
, [0, 0], [-772605/1048576, -1545209/2097152]]]], [[1, 9, 2, 3, 3], [v < 0, 
And(-v < u,u < (v^2+1)^(1/2)), x = -1, And(-u^2+v^2 < y,y < u^2-v^2), And(-(-u
^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1, -1], [0, 0], [-1/4194304, -1/4194304]]
]], [[1, 9, 2, 3, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, And(-u^2+
v^2 < y,y < u^2-v^2), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1, -1], [0, 0], [193151/262144, 772605/
1048576]]]], [[1, 9, 2, 3, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1,
And(-u^2+v^2 < y,y < u^2-v^2), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1,
-1], [1265743/1048576, 1265743/1048576], [-1, -1], [0, 0], [2, 2]]]], [[2, 6,
3, 1, 1], [v = 0, u = 0, And(-1 < x,x < 1), y < -1-x, z < -1], [regular_chain,
[[0, 0], [0, 0], [0, 0], [-2, -2], [-2, -2]]]], [[2, 6, 3, 1, 2], [v = 0, u =
0, And(-1 < x,x < 1), y < -1-x, z = -1], [regular_chain, [[0, 0], [0, 0], [0,
0], [-2, -2], [-1, -1]]]], [[2, 6, 3, 1, 3], [v = 0, u = 0, And(-1 < x,x < 1),
y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [0, 0], [-2, -2
], [0, 0]]]], [[2, 6, 3, 1, 4], [v = 0, u = 0, And(-1 < x,x < 1), y < -1-x, z
= 1], [regular_chain, [[0, 0], [0, 0], [0, 0], [-2, -2], [1, 1]]]], [[2, 6, 3,
1, 5], [v = 0, u = 0, And(-1 < x,x < 1), y < -1-x, 1 < z], [regular_chain, [[0
, 0], [0, 0], [0, 0], [-2, -2], [2, 2]]]], [[2, 11, 2, 5, 1], [v = 0, 2^(1/2)
< u, x = -1, u^2 < y, z = z], [regular_chain, [[0, 0], [3, 3], [-1, -1], [10,
10], [0, 0]]]], [[1, 11, 6, 2, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(
1/2)), x = 1, y = u^2-v^2-2, z = z], [regular_chain, [[-1, -1], [3299097/
2097152, 3299097/2097152], [1, 1], [-1101541/2097152, -275385/524288], [0, 0]]
]], [[2, 3, 6, 3, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = 1, And(u^2-2 < y,y
< -u^2+2), z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/
1048576], [1, 1], [0, 0], [0, 0]]]], [[3, 3, 1, 2, 1], [0 < v, And(-(v^2+2)^(1
/2) < u,u < -(v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, z = z], [regular_chain,
[[1, 1], [-6598195/4194304, -6598195/4194304], [-2, -2], [-2594959/1048576, -\
1297479/524288], [0, 0]]]], [[3, 7, 6, 3, 1], [0 < v, And(-v < u,u < v), x = 1
, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z < -(-u^2+v^2+1)^(1/2)], [regular_chain,
[[1, 1], [0, 0], [1, 1], [0, 0], [-3, -3]]]], [[3, 7, 6, 3, 2], [0 < v, And(-v
< u,u < v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = -(-u^2+v^2+1)^(1/2)]
, [regular_chain, [[1, 1], [0, 0], [1, 1], [0, 0], [-1482911/1048576, -741455/
524288]]]], [[3, 7, 6, 3, 3], [0 < v, And(-v < u,u < v), x = 1, And(u^2-v^2-2
< y,y < -u^2+v^2+2), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [1, 1], [0, 0], [0, 0]]]], [[3, 7, 6, 3, 4], [
0 < v, And(-v < u,u < v), x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = (-u^2+
v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [1, 1], [0, 0], [741455/524288
, 1482911/1048576]]]], [[3, 7, 6, 3, 5], [0 < v, And(-v < u,u < v), x = 1, And
(u^2-v^2-2 < y,y < -u^2+v^2+2), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1,
1], [0, 0], [1, 1], [0, 0], [3, 3]]]], [[1, 4, 2, 3, 1], [v < 0, u = -(v^2+1)^
(1/2), x = -1, And(-1 < y,y < 1), z < 0], [regular_chain, [[-1, -1], [-1482911
/1048576, -741455/524288], [-1, -1], [0, 0], [-1, -1]]]], [[1, 4, 2, 3, 2], [v
< 0, u = -(v^2+1)^(1/2), x = -1, And(-1 < y,y < 1), z = 0], [regular_chain, [[
-1, -1], [-1482911/1048576, -741455/524288], [-1, -1], [0, 0], [0, 0]]]], [[1,
4, 2, 3, 3], [v < 0, u = -(v^2+1)^(1/2), x = -1, And(-1 < y,y < 1), 0 < z], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1, -1], [0, 0]
, [1, 1]]]], [[1, 9, 2, 4, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1,
y = u^2-v^2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/
1048576, 1265743/1048576], [-1, -1], [239655/524288, 479311/1048576], [-2, -2]
]]], [[1, 9, 2, 4, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y = u^2-
v^2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [-1, -1], [239655/524288, 479311/1048576], [-772605/1048576,
-1545209/2097152]]]], [[1, 9, 2, 4, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x = -1, y = u^2-v^2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1], [
239655/524288, 479311/1048576], [-1/4194304, -1/4194304]]]], [[1, 9, 2, 4, 4],
[v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y = u^2-v^2, z = (-u^2+v^2+1)^(
1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1]
, [239655/524288, 479311/1048576], [193151/262144, 772605/1048576]]]], [[1, 9,
2, 4, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y = u^2-v^2, (-u^2+v^
2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576]
, [-1, -1], [239655/524288, 479311/1048576], [2, 2]]]], [[2, 6, 2, 3, 1], [v =
0, u = 0, x = -1, 0 < y, z < -1], [regular_chain, [[0, 0], [0, 0], [-1, -1], [
1, 1], [-2, -2]]]], [[2, 6, 2, 3, 2], [v = 0, u = 0, x = -1, 0 < y, z = -1], [
regular_chain, [[0, 0], [0, 0], [-1, -1], [1, 1], [-1, -1]]]], [[2, 6, 2, 3, 3
], [v = 0, u = 0, x = -1, 0 < y, And(-1 < z,z < 1)], [regular_chain, [[0, 0],
[0, 0], [-1, -1], [1, 1], [0, 0]]]], [[2, 6, 2, 3, 4], [v = 0, u = 0, x = -1,
0 < y, z = 1], [regular_chain, [[0, 0], [0, 0], [-1, -1], [1, 1], [1, 1]]]], [
[2, 6, 2, 3, 5], [v = 0, u = 0, x = -1, 0 < y, 1 < z], [regular_chain, [[0, 0]
, [0, 0], [-1, -1], [1, 1], [2, 2]]]], [[2, 11, 2, 4, 1], [v = 0, 2^(1/2) < u,
x = -1, y = u^2, z = z], [regular_chain, [[0, 0], [3, 3], [-1, -1], [9, 9], [0
, 0]]]], [[1, 11, 6, 3, 1], [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)),
x = 1, And(u^2-v^2-2 < y,y < -u^2+v^2+2), z = z], [regular_chain, [[-1, -1], [
3299097/2097152, 3299097/2097152], [1, 1], [0, 0], [0, 0]]]], [[2, 3, 5, 5, 1]
, [v = 0, And(-2^(1/2) < u,u < -1), And(u^2-1 < x,x < 1), x-u^2+1 < y, z = z],
[regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [1527887/
2097152, 1527887/2097152], [2, 2], [0, 0]]]], [[3, 3, 1, 5, 1], [0 < v, And(-(
v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, u^2-v^2-x-1 < y, z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-2, -2], [4, 4]
, [0, 0]]]], [[3, 7, 6, 2, 1], [0 < v, And(-v < u,u < v), x = 1, y = u^2-v^2-2
, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [1, 1], [-3, -3],
[-3, -3]]]], [[3, 7, 6, 2, 2], [0 < v, And(-v < u,u < v), x = 1, y = u^2-v^2-2
, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [1, 1], [-3, -3],
[-1482911/1048576, -741455/524288]]]], [[3, 7, 6, 2, 3], [0 < v, And(-v < u,u
< v), x = 1, y = u^2-v^2-2, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2)
)], [regular_chain, [[1, 1], [0, 0], [1, 1], [-3, -3], [0, 0]]]], [[3, 7, 6, 2
, 4], [0 < v, And(-v < u,u < v), x = 1, y = u^2-v^2-2, z = (-u^2+v^2+1)^(1/2)]
, [regular_chain, [[1, 1], [0, 0], [1, 1], [-3, -3], [741455/524288, 1482911/
1048576]]]], [[3, 7, 6, 2, 5], [0 < v, And(-v < u,u < v), x = 1, y = u^2-v^2-2
, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [1, 1], [-3, -3],
[3, 3]]]], [[1, 4, 2, 4, 1], [v < 0, u = -(v^2+1)^(1/2), x = -1, y = 1, z < 0]
, [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1, -1], [1,
1], [-1, -1]]]], [[1, 4, 2, 4, 2], [v < 0, u = -(v^2+1)^(1/2), x = -1, y = 1,
z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-1, -1
], [1, 1], [0, 0]]]], [[1, 4, 2, 4, 3], [v < 0, u = -(v^2+1)^(1/2), x = -1, y
= 1, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [-\
1, -1], [1, 1], [1, 1]]]], [[1, 9, 2, 1, 1], [v < 0, And(-v < u,u < (v^2+1)^(1
/2)), x = -1, y < -u^2+v^2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1
], [1265743/1048576, 1265743/1048576], [-1, -1], [-2, -2], [-2, -2]]]], [[1, 9
, 2, 1, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y < -u^2+v^2, z = -
(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-1, -1], [-2, -2], [-772605/1048576, -1545209/2097152]]]], [[1, 9,
2, 1, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y < -u^2+v^2, And(-(-
u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1, -1], [-2, -2], [-1/4194304, -1/4194304
]]]], [[1, 9, 2, 1, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y < -u^
2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [-1, -1], [-2, -2], [193151/262144, 772605/1048576]]]], [[1,
9, 2, 1, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y < -u^2+v^2, (-u^
2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-1, -1], [-2, -2], [2, 2]]]], [[2, 6, 3, 3, 1], [v = 0, u = 0, And(
-1 < x,x < 1), And(-1-x < y,y < x+1), z < -1], [regular_chain, [[0, 0], [0, 0]
, [0, 0], [0, 0], [-2, -2]]]], [[2, 6, 3, 3, 2], [v = 0, u = 0, And(-1 < x,x <
1), And(-1-x < y,y < x+1), z = -1], [regular_chain, [[0, 0], [0, 0], [0, 0], [
0, 0], [-1, -1]]]], [[2, 6, 3, 3, 3], [v = 0, u = 0, And(-1 < x,x < 1), And(-1
-x < y,y < x+1), And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [0, 0],
[0, 0], [0, 0]]]], [[2, 6, 3, 3, 4], [v = 0, u = 0, And(-1 < x,x < 1), And(-1-
x < y,y < x+1), z = 1], [regular_chain, [[0, 0], [0, 0], [0, 0], [0, 0], [1, 1
]]]], [[2, 6, 3, 3, 5], [v = 0, u = 0, And(-1 < x,x < 1), And(-1-x < y,y < x+1
), 1 < z], [regular_chain, [[0, 0], [0, 0], [0, 0], [0, 0], [2, 2]]]], [[2, 11
, 2, 3, 1], [v = 0, 2^(1/2) < u, x = -1, And(-u^2 < y,y < u^2), z = z], [
regular_chain, [[0, 0], [3, 3], [-1, -1], [0, 0], [0, 0]]]], [[1, 11, 6, 4, 1]
, [v < 0, And((v^2+1)^(1/2) < u,u < (v^2+2)^(1/2)), x = 1, y = -u^2+v^2+2, z =
z], [regular_chain, [[-1, -1], [3299097/2097152, 3299097/2097152], [1, 1], [
275385/524288, 550771/1048576], [0, 0]]]], [[2, 3, 6, 1, 1], [v = 0, And(-2^(1
/2) < u,u < -1), x = 1, y < u^2-2, z = z], [regular_chain, [[0, 0], [-1265743/
1048576, -1265743/1048576], [1, 1], [-2, -2], [0, 0]]]], [[3, 3, 1, 4, 1], [0
< v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z =
z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-2, -2], [
1297479/524288, 2594959/1048576], [0, 0]]]], [[3, 7, 6, 1, 1], [0 < v, And(-v
< u,u < v), x = 1, y < u^2-v^2-2, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [0, 0], [1, 1], [-4, -4], [-3, -3]]]], [[3, 7, 6, 1, 2], [0 < v, And(-v
< u,u < v), x = 1, y < u^2-v^2-2, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [0, 0], [1, 1], [-4, -4], [-1482911/1048576, -741455/524288]]]], [[3, 7
, 6, 1, 3], [0 < v, And(-v < u,u < v), x = 1, y < u^2-v^2-2, And(-(-u^2+v^2+1)
^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [1, 1],
[-4, -4], [0, 0]]]], [[3, 7, 6, 1, 4], [0 < v, And(-v < u,u < v), x = 1, y < u
^2-v^2-2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [1, 1], [-\
4, -4], [741455/524288, 1482911/1048576]]]], [[3, 7, 6, 1, 5], [0 < v, And(-v
< u,u < v), x = 1, y < u^2-v^2-2, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1
, 1], [0, 0], [1, 1], [-4, -4], [3, 3]]]], [[1, 4, 2, 5, 1], [v < 0, u = -(v^2
+1)^(1/2), x = -1, 1 < y, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576
, -741455/524288], [-1, -1], [2, 2], [-1, -1]]]], [[1, 4, 2, 5, 2], [v < 0, u
= -(v^2+1)^(1/2), x = -1, 1 < y, z = 0], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [-1, -1], [2, 2], [0, 0]]]], [[1, 4, 2, 5, 3], [v <
0, u = -(v^2+1)^(1/2), x = -1, 1 < y, 0 < z], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [-1, -1], [2, 2], [1, 1]]]], [[1, 9, 2, 2, 1
], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, z < -(-u^2+v^2
+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1
, -1], [-479311/1048576, -239655/524288], [-2, -2]]]], [[1, 9, 2, 2, 2], [v <
0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, z = -(-u^2+v^2+1)^(1/2
)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1], [
-479311/1048576, -239655/524288], [-772605/1048576, -1545209/2097152]]]], [[1,
9, 2, 2, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, And(
-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-1, -1], [-479311/1048576, -239655/524288]
, [-1/4194304, -1/4194304]]]], [[1, 9, 2, 2, 4], [v < 0, And(-v < u,u < (v^2+1
)^(1/2)), x = -1, y = -u^2+v^2, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1,
-1], [1265743/1048576, 1265743/1048576], [-1, -1], [-479311/1048576, -239655/
524288], [193151/262144, 772605/1048576]]]], [[1, 9, 2, 2, 5], [v < 0, And(-v
< u,u < (v^2+1)^(1/2)), x = -1, y = -u^2+v^2, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-1, -1], [-\
479311/1048576, -239655/524288], [2, 2]]]], [[2, 6, 3, 2, 1], [v = 0, u = 0, 
And(-1 < x,x < 1), y = -1-x, z < -1], [regular_chain, [[0, 0], [0, 0], [0, 0],
[-1, -1], [-2, -2]]]], [[2, 6, 3, 2, 2], [v = 0, u = 0, And(-1 < x,x < 1), y =
-1-x, z = -1], [regular_chain, [[0, 0], [0, 0], [0, 0], [-1, -1], [-1, -1]]]],
[[2, 6, 3, 2, 3], [v = 0, u = 0, And(-1 < x,x < 1), y = -1-x, And(-1 < z,z < 1
)], [regular_chain, [[0, 0], [0, 0], [0, 0], [-1, -1], [0, 0]]]], [[2, 6, 3, 2
, 4], [v = 0, u = 0, And(-1 < x,x < 1), y = -1-x, z = 1], [regular_chain, [[0,
0], [0, 0], [0, 0], [-1, -1], [1, 1]]]], [[2, 6, 3, 2, 5], [v = 0, u = 0, And(
-1 < x,x < 1), y = -1-x, 1 < z], [regular_chain, [[0, 0], [0, 0], [0, 0], [-1,
-1], [2, 2]]]], [[2, 11, 2, 2, 1], [v = 0, 2^(1/2) < u, x = -1, y = -u^2, z =
z], [regular_chain, [[0, 0], [3, 3], [-1, -1], [-9, -9], [0, 0]]]], [[1, 5, 1,
5, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, u^2-v^2-x-1 < y, z < -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [3, 3], [-2, -2]]]], [[1, 5, 1, 5, 2], [v < 0, And(-(v^2+1
)^(1/2) < u,u < v), x < -1, u^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [3,
3], [-772605/1048576, -1545209/2097152]]]], [[1, 5, 1, 5, 3], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x < -1, u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z
< (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743
/1048576], [-2, -2], [3, 3], [-1/4194304, -1/4194304]]]], [[1, 5, 1, 5, 4], [v
< 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, u^2-v^2-x-1 < y, z = (-u^2+v^2+1)^
(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2,
-2], [3, 3], [193151/262144, 772605/1048576]]]], [[1, 5, 1, 5, 5], [v < 0, And
(-(v^2+1)^(1/2) < u,u < v), x < -1, u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z],
[regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [3,
3], [2, 2]]]], [[1, 9, 1, 3, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1
, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [0, 0]
, [-2, -2]]]], [[1, 9, 1, 3, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1
, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [0, 0]
, [-772605/1048576, -1545209/2097152]]]], [[1, 9, 1, 3, 3], [v < 0, And(-v < u
,u < (v^2+1)^(1/2)), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+
v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [1265743
/1048576, 1265743/1048576], [-2, -2], [0, 0], [-1/4194304, -1/4194304]]]], [[1
, 9, 1, 3, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, And(x-u^2+v^2+1
< y,y < u^2-v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-2, -2], [0, 0], [193151/262144, 772605/
1048576]]]], [[1, 9, 1, 3, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1,
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain,
[[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [0, 0], [2, 2]]]], [[
2, 6, 5, 4, 1], [v = 0, u = 0, 1 < x, y = x+1, z < -1], [regular_chain, [[0, 0
], [0, 0], [2, 2], [3, 3], [-2, -2]]]], [[2, 6, 5, 4, 2], [v = 0, u = 0, 1 < x
, y = x+1, z = -1], [regular_chain, [[0, 0], [0, 0], [2, 2], [3, 3], [-1, -1]]
]], [[2, 6, 5, 4, 3], [v = 0, u = 0, 1 < x, y = x+1, And(-1 < z,z < 1)], [
regular_chain, [[0, 0], [0, 0], [2, 2], [3, 3], [0, 0]]]], [[2, 6, 5, 4, 4], [
v = 0, u = 0, 1 < x, y = x+1, z = 1], [regular_chain, [[0, 0], [0, 0], [2, 2],
[3, 3], [1, 1]]]], [[2, 6, 5, 4, 5], [v = 0, u = 0, 1 < x, y = x+1, 1 < z], [
regular_chain, [[0, 0], [0, 0], [2, 2], [3, 3], [2, 2]]]], [[2, 10, 2, 5, 1],
[v = 0, u = 2^(1/2), x = -1, 2 < y, z = z], [regular_chain, [[0, 0], [741455/
524288, 1482911/1048576], [-1, -1], [3, 3], [0, 0]]]], [[1, 12, 3, 4, 1], [v <
0, u = (v^2+2)^(1/2), And(-1 < x,x < 1), y = 1-x, z = z], [regular_chain, [[-1
, -1], [908093/524288, 1816187/1048576], [0, 0], [1, 1], [0, 0]]]], [[2, 3, 3,
2, 1], [v = 0, And(-2^(1/2) < u,u < -1), And(-1 < x,x < u^2-1), y = x-u^2+1, z
= z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [-284633/
1048576, -284633/1048576], [-95493/131072, -1527887/2097152], [0, 0]]]], [[3,
3, 2, 3, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = -1, And(-
u^2+v^2 < y,y < u^2-v^2), z = z], [regular_chain, [[1, 1], [-6598195/4194304,
-6598195/4194304], [-1, -1], [0, 0], [0, 0]]]], [[3, 6, 5, 1, 1], [0 < v, u =
-v, 1 < x, y < -1-x, z < -1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [-4,
-4], [-2, -2]]]], [[3, 6, 5, 1, 2], [0 < v, u = -v, 1 < x, y < -1-x, z = -1],
[regular_chain, [[1, 1], [-1, -1], [2, 2], [-4, -4], [-1, -1]]]], [[3, 6, 5, 1
, 3], [0 < v, u = -v, 1 < x, y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[1
, 1], [-1, -1], [2, 2], [-4, -4], [0, 0]]]], [[3, 6, 5, 1, 4], [0 < v, u = -v,
1 < x, y < -1-x, z = 1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [-4, -4],
[1, 1]]]], [[3, 6, 5, 1, 5], [0 < v, u = -v, 1 < x, y < -1-x, 1 < z], [
regular_chain, [[1, 1], [-1, -1], [2, 2], [-4, -4], [2, 2]]]], [[1, 5, 1, 4, 1
], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y = u^2-v^2-x-1, z < -(-u^2+
v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576]
, [-2, -2], [763943/524288, 1527887/1048576], [-2, -2]]]], [[1, 5, 1, 4, 2], [
v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y = u^2-v^2-x-1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-\
2, -2], [763943/524288, 1527887/1048576], [-772605/1048576, -1545209/2097152]]
]], [[1, 5, 1, 4, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y = u^2-v
^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain,
[[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [763943/524288, 
1527887/1048576], [-1/4194304, -1/4194304]]]], [[1, 5, 1, 4, 4], [v < 0, And(-
(v^2+1)^(1/2) < u,u < v), x < -1, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [
763943/524288, 1527887/1048576], [193151/262144, 772605/1048576]]]], [[1, 5, 1
, 4, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y = u^2-v^2-x-1, (-u^2
+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [763943/524288, 1527887/1048576], [2, 2]]]], [[1, 9, 1, 2,
1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, z < -(-u^2
+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576],
[-2, -2], [-1527887/1048576, -763943/524288], [-2, -2]]]], [[1, 9, 1, 2, 2], [
v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, z = -(-u^2+v^2+
1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2,
-2], [-1527887/1048576, -763943/524288], [-772605/1048576, -1545209/2097152]]]
], [[1, 9, 1, 2, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = x-u^2+
v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [-1527887/1048576, -\
763943/524288], [-1/4194304, -1/4194304]]]], [[1, 9, 1, 2, 4], [v < 0, And(-v
< u,u < (v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [-\
1527887/1048576, -763943/524288], [193151/262144, 772605/1048576]]]], [[1, 9,
1, 2, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = x-u^2+v^2+1, (-u^
2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-2, -2], [-1527887/1048576, -763943/524288], [2, 2]]]], [[2, 6, 5,
5, 1], [v = 0, u = 0, 1 < x, x+1 < y, z < -1], [regular_chain, [[0, 0], [0, 0]
, [2, 2], [4, 4], [-2, -2]]]], [[2, 6, 5, 5, 2], [v = 0, u = 0, 1 < x, x+1 < y
, z = -1], [regular_chain, [[0, 0], [0, 0], [2, 2], [4, 4], [-1, -1]]]], [[2,
6, 5, 5, 3], [v = 0, u = 0, 1 < x, x+1 < y, And(-1 < z,z < 1)], [regular_chain
, [[0, 0], [0, 0], [2, 2], [4, 4], [0, 0]]]], [[2, 6, 5, 5, 4], [v = 0, u = 0,
1 < x, x+1 < y, z = 1], [regular_chain, [[0, 0], [0, 0], [2, 2], [4, 4], [1, 1
]]]], [[2, 6, 5, 5, 5], [v = 0, u = 0, 1 < x, x+1 < y, 1 < z], [regular_chain,
[[0, 0], [0, 0], [2, 2], [4, 4], [2, 2]]]], [[2, 10, 3, 1, 1], [v = 0, u = 2^(
1/2), And(-1 < x,x < 1), y < x-1, z = z], [regular_chain, [[0, 0], [741455/
524288, 1482911/1048576], [0, 0], [-2, -2], [0, 0]]]], [[1, 12, 3, 3, 1], [v <
0, u = (v^2+2)^(1/2), And(-1 < x,x < 1), And(x-1 < y,y < 1-x), z = z], [
regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [0, 0], [0, 0], [0
, 0]]]], [[2, 3, 3, 1, 1], [v = 0, And(-2^(1/2) < u,u < -1), And(-1 < x,x < u^
2-1), y < x-u^2+1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -\
1265743/1048576], [-284633/1048576, -284633/1048576], [-2, -2], [0, 0]]]], [[3
, 3, 2, 4, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = -1, y =
u^2-v^2, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304]
, [-1, -1], [773191/524288, 1546383/1048576], [0, 0]]]], [[3, 6, 5, 2, 1], [0
< v, u = -v, 1 < x, y = -1-x, z < -1], [regular_chain, [[1, 1], [-1, -1], [2,
2], [-3, -3], [-2, -2]]]], [[3, 6, 5, 2, 2], [0 < v, u = -v, 1 < x, y = -1-x,
z = -1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [-3, -3], [-1, -1]]]], [[3
, 6, 5, 2, 3], [0 < v, u = -v, 1 < x, y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[1, 1], [-1, -1], [2, 2], [-3, -3], [0, 0]]]], [[3, 6, 5, 2, 4
], [0 < v, u = -v, 1 < x, y = -1-x, z = 1], [regular_chain, [[1, 1], [-1, -1],
[2, 2], [-3, -3], [1, 1]]]], [[3, 6, 5, 2, 5], [0 < v, u = -v, 1 < x, y = -1-x
, 1 < z], [regular_chain, [[1, 1], [-1, -1], [2, 2], [-3, -3], [2, 2]]]], [[1,
5, 1, 3, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, And(x-u^2+v^2+1 <
y,y < u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-\
1265743/1048576, -1265743/1048576], [-2, -2], [0, 0], [-2, -2]]]], [[1, 5, 1,
3, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, And(x-u^2+v^2+1 < y,y <
u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [0, 0], [-772605/1048576, -1545209/
2097152]]]], [[1, 5, 1, 3, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1,
And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^
2+1)^(1/2))], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576],
[-2, -2], [0, 0], [-1/4194304, -1/4194304]]]], [[1, 5, 1, 3, 4], [v < 0, And(-
(v^2+1)^(1/2) < u,u < v), x < -1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = (-
u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [0, 0], [193151/262144, 772605/1048576]]]], [[1, 5, 1, 3,
5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, And(x-u^2+v^2+1 < y,y < u^2
-v^2-x-1), (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/
1048576, -1265743/1048576], [-2, -2], [0, 0], [2, 2]]]], [[1, 9, 1, 5, 1], [v
< 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, u^2-v^2-x-1 < y, z < -(-u^2+v^2+1)
^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -\
2], [3, 3], [-2, -2]]]], [[1, 9, 1, 5, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2
)), x < -1, u^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -\
1], [1265743/1048576, 1265743/1048576], [-2, -2], [3, 3], [-772605/1048576, -\
1545209/2097152]]]], [[1, 9, 1, 5, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x < -1, u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))],
[regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [3, 3
], [-1/4194304, -1/4194304]]]], [[1, 9, 1, 5, 4], [v < 0, And(-v < u,u < (v^2+
1)^(1/2)), x < -1, u^2-v^2-x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [
[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [3, 3], [193151/262144
, 772605/1048576]]]], [[1, 9, 1, 5, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x < -1, u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-2, -2], [3, 3], [2, 2]]]], [[2, 6, 5, 2,
1], [v = 0, u = 0, 1 < x, y = -1-x, z < -1], [regular_chain, [[0, 0], [0, 0],
[2, 2], [-3, -3], [-2, -2]]]], [[2, 6, 5, 2, 2], [v = 0, u = 0, 1 < x, y = -1-
x, z = -1], [regular_chain, [[0, 0], [0, 0], [2, 2], [-3, -3], [-1, -1]]]], [[
2, 6, 5, 2, 3], [v = 0, u = 0, 1 < x, y = -1-x, And(-1 < z,z < 1)], [
regular_chain, [[0, 0], [0, 0], [2, 2], [-3, -3], [0, 0]]]], [[2, 6, 5, 2, 4],
[v = 0, u = 0, 1 < x, y = -1-x, z = 1], [regular_chain, [[0, 0], [0, 0], [2, 2
], [-3, -3], [1, 1]]]], [[2, 6, 5, 2, 5], [v = 0, u = 0, 1 < x, y = -1-x, 1 <
z], [regular_chain, [[0, 0], [0, 0], [2, 2], [-3, -3], [2, 2]]]], [[2, 10, 3,
2, 1], [v = 0, u = 2^(1/2), And(-1 < x,x < 1), y = x-1, z = z], [regular_chain
, [[0, 0], [741455/524288, 1482911/1048576], [0, 0], [-1, -1], [0, 0]]]], [[1,
12, 3, 2, 1], [v < 0, u = (v^2+2)^(1/2), And(-1 < x,x < 1), y = x-1, z = z], [
regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [0, 0], [-1, -1],
[0, 0]]]], [[2, 3, 3, 4, 1], [v = 0, And(-2^(1/2) < u,u < -1), And(-1 < x,x <
u^2-1), y = u^2-x-1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -\
1265743/1048576], [-284633/1048576, -284633/1048576], [763943/1048576, 95493/
131072], [0, 0]]]], [[3, 3, 2, 1, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2
+1)^(1/2)), x = -1, y < -u^2+v^2, z = z], [regular_chain, [[1, 1], [-6598195/
4194304, -6598195/4194304], [-1, -1], [-3, -3], [0, 0]]]], [[3, 6, 5, 3, 1], [
0 < v, u = -v, 1 < x, And(-1-x < y,y < x+1), z < -1], [regular_chain, [[1, 1],
[-1, -1], [2, 2], [0, 0], [-2, -2]]]], [[3, 6, 5, 3, 2], [0 < v, u = -v, 1 < x
, And(-1-x < y,y < x+1), z = -1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [
0, 0], [-1, -1]]]], [[3, 6, 5, 3, 3], [0 < v, u = -v, 1 < x, And(-1-x < y,y <
x+1), And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [2, 2], [0, 0], [
0, 0]]]], [[3, 6, 5, 3, 4], [0 < v, u = -v, 1 < x, And(-1-x < y,y < x+1), z =
1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [0, 0], [1, 1]]]], [[3, 6, 5, 3
, 5], [0 < v, u = -v, 1 < x, And(-1-x < y,y < x+1), 1 < z], [regular_chain, [[
1, 1], [-1, -1], [2, 2], [0, 0], [2, 2]]]], [[1, 5, 1, 2, 1], [v < 0, And(-(v^
2+1)^(1/2) < u,u < v), x < -1, y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [-\
1527887/1048576, -763943/524288], [-2, -2]]]], [[1, 5, 1, 2, 2], [v < 0, And(-
(v^2+1)^(1/2) < u,u < v), x < -1, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [-\
1527887/1048576, -763943/524288], [-772605/1048576, -1545209/2097152]]]], [[1,
5, 1, 2, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y = x-u^2+v^2+1, 
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1
], [-1265743/1048576, -1265743/1048576], [-2, -2], [-1527887/1048576, -763943/
524288], [-1/4194304, -1/4194304]]]], [[1, 5, 1, 2, 4], [v < 0, And(-(v^2+1)^(
1/2) < u,u < v), x < -1, y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[-1, -1], [-1265743/1048576, -1265743/1048576], [-2, -2], [-\
1527887/1048576, -763943/524288], [193151/262144, 772605/1048576]]]], [[1, 5,
1, 2, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y = x-u^2+v^2+1, (-u^
2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743/
1048576], [-2, -2], [-1527887/1048576, -763943/524288], [2, 2]]]], [[1, 9, 1,
4, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z < -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-2, -2], [763943/524288, 1527887/1048576], [-2, -2]]]], [[1, 9, 1,
4, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z = -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-2, -2], [763943/524288, 1527887/1048576], [-772605/1048576, -\
1545209/2097152]]]], [[1, 9, 1, 4, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)),
x < -1, y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))],
[regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-2, -2], [
763943/524288, 1527887/1048576], [-1/4194304, -1/4194304]]]], [[1, 9, 1, 4, 4]
, [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x-1, z = (-u^2+v^
2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/1048576], [-\
2, -2], [763943/524288, 1527887/1048576], [193151/262144, 772605/1048576]]]],
[[1, 9, 1, 4, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y = u^2-v^2-x
-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [-2, -2], [763943/524288, 1527887/1048576], [2, 2]]]], [[2,
6, 5, 3, 1], [v = 0, u = 0, 1 < x, And(-1-x < y,y < x+1), z < -1], [
regular_chain, [[0, 0], [0, 0], [2, 2], [0, 0], [-2, -2]]]], [[2, 6, 5, 3, 2],
[v = 0, u = 0, 1 < x, And(-1-x < y,y < x+1), z = -1], [regular_chain, [[0, 0],
[0, 0], [2, 2], [0, 0], [-1, -1]]]], [[2, 6, 5, 3, 3], [v = 0, u = 0, 1 < x, 
And(-1-x < y,y < x+1), And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [2
, 2], [0, 0], [0, 0]]]], [[2, 6, 5, 3, 4], [v = 0, u = 0, 1 < x, And(-1-x < y,
y < x+1), z = 1], [regular_chain, [[0, 0], [0, 0], [2, 2], [0, 0], [1, 1]]]],
[[2, 6, 5, 3, 5], [v = 0, u = 0, 1 < x, And(-1-x < y,y < x+1), 1 < z], [
regular_chain, [[0, 0], [0, 0], [2, 2], [0, 0], [2, 2]]]], [[2, 10, 3, 3, 1],
[v = 0, u = 2^(1/2), And(-1 < x,x < 1), And(x-1 < y,y < 1-x), z = z], [
regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [0, 0], [0, 0], [0,
0]]]], [[1, 12, 3, 1, 1], [v < 0, u = (v^2+2)^(1/2), And(-1 < x,x < 1), y < x-\
1, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [0, 0]
, [-2, -2], [0, 0]]]], [[2, 3, 3, 3, 1], [v = 0, And(-2^(1/2) < u,u < -1), And
(-1 < x,x < u^2-1), And(x-u^2+1 < y,y < u^2-x-1), z = z], [regular_chain, [[0,
0], [-1265743/1048576, -1265743/1048576], [-284633/1048576, -284633/1048576],
[-1/4194304, -1/4194304], [0, 0]]]], [[3, 3, 2, 2, 1], [0 < v, And(-(v^2+2)^(1
/2) < u,u < -(v^2+1)^(1/2)), x = -1, y = -u^2+v^2, z = z], [regular_chain, [[1
, 1], [-6598195/4194304, -6598195/4194304], [-1, -1], [-1546383/1048576, -\
773191/524288], [0, 0]]]], [[3, 6, 5, 4, 1], [0 < v, u = -v, 1 < x, y = x+1, z
< -1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [3, 3], [-2, -2]]]], [[3, 6,
5, 4, 2], [0 < v, u = -v, 1 < x, y = x+1, z = -1], [regular_chain, [[1, 1], [-\
1, -1], [2, 2], [3, 3], [-1, -1]]]], [[3, 6, 5, 4, 3], [0 < v, u = -v, 1 < x,
y = x+1, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [2, 2], [3, 3]
, [0, 0]]]], [[3, 6, 5, 4, 4], [0 < v, u = -v, 1 < x, y = x+1, z = 1], [
regular_chain, [[1, 1], [-1, -1], [2, 2], [3, 3], [1, 1]]]], [[3, 6, 5, 4, 5],
[0 < v, u = -v, 1 < x, y = x+1, 1 < z], [regular_chain, [[1, 1], [-1, -1], [2,
2], [3, 3], [2, 2]]]], [[1, 12, 4, 3, 1], [v < 0, u = (v^2+2)^(1/2), x = 1, 0
< y, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [1,
1], [1, 1], [0, 0]]]], [[2, 3, 4, 1, 1], [v = 0, And(-2^(1/2) < u,u < -1), x =
u^2-1, y < 0, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/
1048576], [239655/524288, 479311/1048576], [-1, -1], [0, 0]]]], [[3, 3, 3, 2,
1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2
-1), y = x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -\
6598195/4194304], [-275385/1048576, -275385/1048576], [-1546383/2097152, -\
773191/1048576], [0, 0]]]], [[3, 6, 5, 5, 1], [0 < v, u = -v, 1 < x, x+1 < y,
z < -1], [regular_chain, [[1, 1], [-1, -1], [2, 2], [4, 4], [-2, -2]]]], [[3,
6, 5, 5, 2], [0 < v, u = -v, 1 < x, x+1 < y, z = -1], [regular_chain, [[1, 1],
[-1, -1], [2, 2], [4, 4], [-1, -1]]]], [[3, 6, 5, 5, 3], [0 < v, u = -v, 1 < x
, x+1 < y, And(-1 < z,z < 1)], [regular_chain, [[1, 1], [-1, -1], [2, 2], [4,
4], [0, 0]]]], [[3, 6, 5, 5, 4], [0 < v, u = -v, 1 < x, x+1 < y, z = 1], [
regular_chain, [[1, 1], [-1, -1], [2, 2], [4, 4], [1, 1]]]], [[3, 6, 5, 5, 5],
[0 < v, u = -v, 1 < x, x+1 < y, 1 < z], [regular_chain, [[1, 1], [-1, -1], [2,
2], [4, 4], [2, 2]]]], [[1, 5, 1, 1, 1], [v < 0, And(-(v^2+1)^(1/2) < u,u < v)
, x < -1, y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1]
, [-1265743/1048576, -1265743/1048576], [-2, -2], [-3, -3], [-2, -2]]]], [[1,
5, 1, 1, 2], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y < x-u^2+v^2+1, z
= -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743/1048576, -1265743
/1048576], [-2, -2], [-3, -3], [-772605/1048576, -1545209/2097152]]]], [[1, 5,
1, 1, 3], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1, y < x-u^2+v^2+1, And(
-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
-1265743/1048576, -1265743/1048576], [-2, -2], [-3, -3], [-1/4194304, -1/
4194304]]]], [[1, 5, 1, 1, 4], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1,
y < x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [-1265743
/1048576, -1265743/1048576], [-2, -2], [-3, -3], [193151/262144, 772605/
1048576]]]], [[1, 5, 1, 1, 5], [v < 0, And(-(v^2+1)^(1/2) < u,u < v), x < -1,
y < x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [-1265743
/1048576, -1265743/1048576], [-2, -2], [-3, -3], [2, 2]]]], [[1, 8, 5, 4, 1],
[v < 0, u = -v, 1 < x, y = x+1, z < -1], [regular_chain, [[-1, -1], [1, 1], [2
, 2], [3, 3], [-2, -2]]]], [[1, 8, 5, 4, 2], [v < 0, u = -v, 1 < x, y = x+1, z
= -1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [3, 3], [-1, -1]]]], [[1, 8,
5, 4, 3], [v < 0, u = -v, 1 < x, y = x+1, And(-1 < z,z < 1)], [regular_chain,
[[-1, -1], [1, 1], [2, 2], [3, 3], [0, 0]]]], [[1, 8, 5, 4, 4], [v < 0, u = -v
, 1 < x, y = x+1, z = 1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [3, 3], [
1, 1]]]], [[1, 8, 5, 4, 5], [v < 0, u = -v, 1 < x, y = x+1, 1 < z], [
regular_chain, [[-1, -1], [1, 1], [2, 2], [3, 3], [2, 2]]]], [[2, 6, 4, 5, 1],
[v = 0, u = 0, x = 1, 2 < y, z < -1], [regular_chain, [[0, 0], [0, 0], [1, 1],
[3, 3], [-2, -2]]]], [[2, 6, 4, 5, 2], [v = 0, u = 0, x = 1, 2 < y, z = -1], [
regular_chain, [[0, 0], [0, 0], [1, 1], [3, 3], [-1, -1]]]], [[2, 6, 4, 5, 3],
[v = 0, u = 0, x = 1, 2 < y, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0,
0], [1, 1], [3, 3], [0, 0]]]], [[2, 6, 4, 5, 4], [v = 0, u = 0, x = 1, 2 < y,
z = 1], [regular_chain, [[0, 0], [0, 0], [1, 1], [3, 3], [1, 1]]]], [[2, 6, 4,
5, 5], [v = 0, u = 0, x = 1, 2 < y, 1 < z], [regular_chain, [[0, 0], [0, 0], [
1, 1], [3, 3], [2, 2]]]], [[2, 10, 2, 1, 1], [v = 0, u = 2^(1/2), x = -1, y <
-2, z = z], [regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [-1, -1
], [-3, -3], [0, 0]]]], [[1, 12, 4, 2, 1], [v < 0, u = (v^2+2)^(1/2), x = 1, y
= 0, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [1,
1], [0, 0], [0, 0]]]], [[2, 3, 3, 5, 1], [v = 0, And(-2^(1/2) < u,u < -1), And
(-1 < x,x < u^2-1), u^2-x-1 < y, z = z], [regular_chain, [[0, 0], [-1265743/
1048576, -1265743/1048576], [-284633/1048576, -284633/1048576], [2, 2], [0, 0]
]]], [[3, 3, 3, 3, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And
(-1 < x,x < u^2-v^2-1), And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-275385/1048576
, -275385/1048576], [0, 0], [0, 0]]]], [[3, 7, 1, 1, 1], [0 < v, And(-v < u,u
< v), x < u^2-v^2-1, y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain
, [[1, 1], [0, 0], [-3, -3], [-2, -2], [-3, -3]]]], [[3, 7, 1, 1, 2], [0 < v,
And(-v < u,u < v), x < u^2-v^2-1, y < x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-3, -3], [-2, -2], [-1482911/1048576, -741455
/524288]]]], [[3, 7, 1, 1, 3], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, y < x
-u^2+v^2+1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [-3, -3], [-2, -2], [0, 0]]]], [[3, 7, 1, 1, 4
], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, y < x-u^2+v^2+1, z = (-u^2+v^2+1)
^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3, -3], [-2, -2], [741455/524288,
1482911/1048576]]]], [[3, 7, 1, 1, 5], [0 < v, And(-v < u,u < v), x < u^2-v^2-\
1, y < x-u^2+v^2+1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0],
[-3, -3], [-2, -2], [3, 3]]]], [[1, 4, 7, 5, 1], [v < 0, u = -(v^2+1)^(1/2), 1
< x, x < y, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [2, 2], [3, 3], [-1, -1]]]], [[1, 4, 7, 5, 2], [v < 0, u = -(v^2+1)^(
1/2), 1 < x, x < y, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -\
741455/524288], [2, 2], [3, 3], [0, 0]]]], [[1, 4, 7, 5, 3], [v < 0, u = -(v^2
+1)^(1/2), 1 < x, x < y, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576,
-741455/524288], [2, 2], [3, 3], [1, 1]]]], [[1, 8, 5, 3, 1], [v < 0, u = -v,
1 < x, And(-1-x < y,y < x+1), z < -1], [regular_chain, [[-1, -1], [1, 1], [2,
2], [0, 0], [-2, -2]]]], [[1, 8, 5, 3, 2], [v < 0, u = -v, 1 < x, And(-1-x < y
,y < x+1), z = -1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [0, 0], [-1, -1
]]]], [[1, 8, 5, 3, 3], [v < 0, u = -v, 1 < x, And(-1-x < y,y < x+1), And(-1 <
z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [2, 2], [0, 0], [0, 0]]]], [[1,
8, 5, 3, 4], [v < 0, u = -v, 1 < x, And(-1-x < y,y < x+1), z = 1], [
regular_chain, [[-1, -1], [1, 1], [2, 2], [0, 0], [1, 1]]]], [[1, 8, 5, 3, 5],
[v < 0, u = -v, 1 < x, And(-1-x < y,y < x+1), 1 < z], [regular_chain, [[-1, -1
], [1, 1], [2, 2], [0, 0], [2, 2]]]], [[2, 6, 5, 1, 1], [v = 0, u = 0, 1 < x,
y < -1-x, z < -1], [regular_chain, [[0, 0], [0, 0], [2, 2], [-4, -4], [-2, -2]
]]], [[2, 6, 5, 1, 2], [v = 0, u = 0, 1 < x, y < -1-x, z = -1], [regular_chain
, [[0, 0], [0, 0], [2, 2], [-4, -4], [-1, -1]]]], [[2, 6, 5, 1, 3], [v = 0, u
= 0, 1 < x, y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [2,
2], [-4, -4], [0, 0]]]], [[2, 6, 5, 1, 4], [v = 0, u = 0, 1 < x, y < -1-x, z =
1], [regular_chain, [[0, 0], [0, 0], [2, 2], [-4, -4], [1, 1]]]], [[2, 6, 5, 1
, 5], [v = 0, u = 0, 1 < x, y < -1-x, 1 < z], [regular_chain, [[0, 0], [0, 0],
[2, 2], [-4, -4], [2, 2]]]], [[2, 10, 2, 2, 1], [v = 0, u = 2^(1/2), x = -1, y
= -2, z = z], [regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [-1,
-1], [-2, -2], [0, 0]]]], [[1, 12, 4, 1, 1], [v < 0, u = (v^2+2)^(1/2), x = 1,
y < 0, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [1
, 1], [-1, -1], [0, 0]]]], [[2, 3, 4, 3, 1], [v = 0, And(-2^(1/2) < u,u < -1),
x = u^2-1, 0 < y, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743
/1048576], [239655/524288, 479311/1048576], [1, 1], [0, 0]]]], [[3, 3, 2, 5, 1
], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = -1, u^2-v^2 < y, z
= z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-1, -1],
[3, 3], [0, 0]]]], [[3, 7, 1, 2, 1], [0 < v, And(-v < u,u < v), x < u^2-v^2-1,
y = x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-\
3, -3], [-1, -1], [-3, -3]]]], [[3, 7, 1, 2, 2], [0 < v, And(-v < u,u < v), x
< u^2-v^2-1, y = x-u^2+v^2+1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1
], [0, 0], [-3, -3], [-1, -1], [-1482911/1048576, -741455/524288]]]], [[3, 7,
1, 2, 3], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, y = x-u^2+v^2+1, And(-(-u^
2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0],
[-3, -3], [-1, -1], [0, 0]]]], [[3, 7, 1, 2, 4], [0 < v, And(-v < u,u < v), x
< u^2-v^2-1, y = x-u^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1]
, [0, 0], [-3, -3], [-1, -1], [741455/524288, 1482911/1048576]]]], [[3, 7, 1,
2, 5], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, y = x-u^2+v^2+1, (-u^2+v^2+1)
^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [-3, -3], [-1, -1], [3, 3]]]], [
[1, 4, 7, 4, 1], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y = x, z < 0], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [2, 2], [2, 2],
[-1, -1]]]], [[1, 4, 7, 4, 2], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y = x, z = 0
], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [2, 2], [2,
2], [0, 0]]]], [[1, 4, 7, 4, 3], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y = x, 0 <
z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [2, 2], [2,
2], [1, 1]]]], [[1, 9, 1, 1, 1], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1
, y < x-u^2+v^2+1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-2, -2], [-3, -3], [-2, -2]]]], [[1, 9, 1,
1, 2], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, z = -(-
u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576, 1265743/
1048576], [-2, -2], [-3, -3], [-772605/1048576, -1545209/2097152]]]], [[1, 9,
1, 1, 3], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1, And(
-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[-1, -1], [
1265743/1048576, 1265743/1048576], [-2, -2], [-3, -3], [-1/4194304, -1/4194304
]]]], [[1, 9, 1, 1, 4], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y < x-u
^2+v^2+1, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[-1, -1], [1265743/1048576
, 1265743/1048576], [-2, -2], [-3, -3], [193151/262144, 772605/1048576]]]], [[
1, 9, 1, 1, 5], [v < 0, And(-v < u,u < (v^2+1)^(1/2)), x < -1, y < x-u^2+v^2+1
, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[-1, -1], [1265743/1048576, 
1265743/1048576], [-2, -2], [-3, -3], [2, 2]]]], [[2, 6, 4, 3, 1], [v = 0, u =
0, x = 1, And(-2 < y,y < 2), z < -1], [regular_chain, [[0, 0], [0, 0], [1, 1],
[0, 0], [-2, -2]]]], [[2, 6, 4, 3, 2], [v = 0, u = 0, x = 1, And(-2 < y,y < 2)
, z = -1], [regular_chain, [[0, 0], [0, 0], [1, 1], [0, 0], [-1, -1]]]], [[2,
6, 4, 3, 3], [v = 0, u = 0, x = 1, And(-2 < y,y < 2), And(-1 < z,z < 1)], [
regular_chain, [[0, 0], [0, 0], [1, 1], [0, 0], [0, 0]]]], [[2, 6, 4, 3, 4], [
v = 0, u = 0, x = 1, And(-2 < y,y < 2), z = 1], [regular_chain, [[0, 0], [0, 0
], [1, 1], [0, 0], [1, 1]]]], [[2, 6, 4, 3, 5], [v = 0, u = 0, x = 1, And(-2 <
y,y < 2), 1 < z], [regular_chain, [[0, 0], [0, 0], [1, 1], [0, 0], [2, 2]]]],
[[2, 10, 2, 3, 1], [v = 0, u = 2^(1/2), x = -1, And(-2 < y,y < 2), z = z], [
regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [-1, -1], [0, 0], [0
, 0]]]], [[1, 12, 3, 5, 1], [v < 0, u = (v^2+2)^(1/2), And(-1 < x,x < 1), 1-x
< y, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [0,
0], [2, 2], [0, 0]]]], [[2, 3, 4, 2, 1], [v = 0, And(-2^(1/2) < u,u < -1), x =
u^2-1, y = 0, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/
1048576], [239655/524288, 479311/1048576], [0, 0], [0, 0]]]], [[3, 3, 3, 1, 1]
, [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1
), y < x-u^2+v^2+1, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -\
6598195/4194304], [-275385/1048576, -275385/1048576], [-2, -2], [0, 0]]]], [[3
, 7, 1, 3, 1], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, And(x-u^2+v^2+1 < y,y
< u^2-v^2-x-1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3
, -3], [0, 0], [-3, -3]]]], [[3, 7, 1, 3, 2], [0 < v, And(-v < u,u < v), x < u
^2-v^2-1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), z = -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-3, -3], [0, 0], [-1482911/1048576, -741455/
524288]]]], [[3, 7, 1, 3, 3], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, And(x-
u^2+v^2+1 < y,y < u^2-v^2-x-1), And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(
1/2))], [regular_chain, [[1, 1], [0, 0], [-3, -3], [0, 0], [0, 0]]]], [[3, 7,
1, 3, 4], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, And(x-u^2+v^2+1 < y,y < u^
2-v^2-x-1), z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3, -3]
, [0, 0], [741455/524288, 1482911/1048576]]]], [[3, 7, 1, 3, 5], [0 < v, And(-
v < u,u < v), x < u^2-v^2-1, And(x-u^2+v^2+1 < y,y < u^2-v^2-x-1), (-u^2+v^2+1
)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [-3, -3], [0, 0], [3, 3]]]], [[
1, 4, 7, 3, 1], [v < 0, u = -(v^2+1)^(1/2), 1 < x, And(-x < y,y < x), z < 0],
[regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [2, 2], [0, 0],
[-1, -1]]]], [[1, 4, 7, 3, 2], [v < 0, u = -(v^2+1)^(1/2), 1 < x, And(-x < y,y
< x), z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [
2, 2], [0, 0], [0, 0]]]], [[1, 4, 7, 3, 3], [v < 0, u = -(v^2+1)^(1/2), 1 < x,
And(-x < y,y < x), 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -\
741455/524288], [2, 2], [0, 0], [1, 1]]]], [[1, 8, 5, 5, 1], [v < 0, u = -v, 1
< x, x+1 < y, z < -1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [4, 4], [-2,
-2]]]], [[1, 8, 5, 5, 2], [v < 0, u = -v, 1 < x, x+1 < y, z = -1], [
regular_chain, [[-1, -1], [1, 1], [2, 2], [4, 4], [-1, -1]]]], [[1, 8, 5, 5, 3
], [v < 0, u = -v, 1 < x, x+1 < y, And(-1 < z,z < 1)], [regular_chain, [[-1, -\
1], [1, 1], [2, 2], [4, 4], [0, 0]]]], [[1, 8, 5, 5, 4], [v < 0, u = -v, 1 < x
, x+1 < y, z = 1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [4, 4], [1, 1]]]
], [[1, 8, 5, 5, 5], [v < 0, u = -v, 1 < x, x+1 < y, 1 < z], [regular_chain, [
[-1, -1], [1, 1], [2, 2], [4, 4], [2, 2]]]], [[2, 6, 4, 4, 1], [v = 0, u = 0,
x = 1, y = 2, z < -1], [regular_chain, [[0, 0], [0, 0], [1, 1], [2, 2], [-2, -\
2]]]], [[2, 6, 4, 4, 2], [v = 0, u = 0, x = 1, y = 2, z = -1], [regular_chain,
[[0, 0], [0, 0], [1, 1], [2, 2], [-1, -1]]]], [[2, 6, 4, 4, 3], [v = 0, u = 0,
x = 1, y = 2, And(-1 < z,z < 1)], [regular_chain, [[0, 0], [0, 0], [1, 1], [2,
2], [0, 0]]]], [[2, 6, 4, 4, 4], [v = 0, u = 0, x = 1, y = 2, z = 1], [
regular_chain, [[0, 0], [0, 0], [1, 1], [2, 2], [1, 1]]]], [[2, 6, 4, 4, 5], [
v = 0, u = 0, x = 1, y = 2, 1 < z], [regular_chain, [[0, 0], [0, 0], [1, 1], [
2, 2], [2, 2]]]], [[2, 10, 2, 4, 1], [v = 0, u = 2^(1/2), x = -1, y = 2, z = z
], [regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [-1, -1], [2, 2]
, [0, 0]]]], [[1, 4, 7, 1, 1], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y < -x, z <
0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [2, 2], [-3
, -3], [-1, -1]]]], [[1, 4, 7, 1, 2], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y < -
x, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [2,
2], [-3, -3], [0, 0]]]], [[1, 4, 7, 1, 3], [v < 0, u = -(v^2+1)^(1/2), 1 < x,
y < -x, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288],
[2, 2], [-3, -3], [1, 1]]]], [[1, 8, 4, 4, 1], [v < 0, u = -v, x = 1, y = 2, z
< -1], [regular_chain, [[-1, -1], [1, 1], [1, 1], [2, 2], [-2, -2]]]], [[1, 8,
4, 4, 2], [v < 0, u = -v, x = 1, y = 2, z = -1], [regular_chain, [[-1, -1], [1
, 1], [1, 1], [2, 2], [-1, -1]]]], [[1, 8, 4, 4, 3], [v < 0, u = -v, x = 1, y
= 2, And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [1, 1], [2, 2], [0
, 0]]]], [[1, 8, 4, 4, 4], [v < 0, u = -v, x = 1, y = 2, z = 1], [
regular_chain, [[-1, -1], [1, 1], [1, 1], [2, 2], [1, 1]]]], [[1, 8, 4, 4, 5],
[v < 0, u = -v, x = 1, y = 2, 1 < z], [regular_chain, [[-1, -1], [1, 1], [1, 1
], [2, 2], [2, 2]]]], [[2, 7, 2, 3, 1], [v = 0, And(0 < u,u < 1), x = -1, And(
-u^2 < y,y < u^2), z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2],
[-1, -1], [0, 0], [-2, -2]]]], [[2, 7, 2, 3, 2], [v = 0, And(0 < u,u < 1), x =
-1, And(-u^2 < y,y < u^2), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2
, 1/2], [-1, -1], [0, 0], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 2,
3, 3], [v = 0, And(0 < u,u < 1), x = -1, And(-u^2 < y,y < u^2), And(-(-u^2+1)^
(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1],
[0, 0], [-1/8388608, -1/8388608]]]], [[2, 7, 2, 3, 4], [v = 0, And(0 < u,u < 1
), x = -1, And(-u^2 < y,y < u^2), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0]
, [1/2, 1/2], [-1, -1], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 7, 2,
3, 5], [v = 0, And(0 < u,u < 1), x = -1, And(-u^2 < y,y < u^2), (-u^2+1)^(1/2)
< z], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [0, 0], [2, 2]]]], [[2, 
10, 5, 1, 1], [v = 0, u = 2^(1/2), 1 < x, y < 1-x, z = z], [regular_chain, [[0
, 0], [741455/524288, 1482911/1048576], [2, 2], [-2, -2], [0, 0]]]], [[1, 12,
1, 5, 1], [v < 0, u = (v^2+2)^(1/2), x < -1, 1-x < y, z = z], [regular_chain,
[[-1, -1], [908093/524288, 1816187/1048576], [-2, -2], [4, 4], [0, 0]]]], [[2,
3, 1, 3, 1], [v = 0, And(-2^(1/2) < u,u < -1), x < -1, And(x-u^2+1 < y,y < u^2
-x-1), z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576],
[-2, -2], [0, 0], [0, 0]]]], [[3, 3, 4, 2, 1], [0 < v, And(-(v^2+2)^(1/2) < u,
u < -(v^2+1)^(1/2)), x = u^2-v^2-1, y = 0, z = z], [regular_chain, [[1, 1], [-\
6598195/4194304, -6598195/4194304], [248903/524288, 497807/1048576], [0, 0], [
0, 0]]]], [[3, 7, 1, 5, 1], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, u^2-v^2-
x-1 < y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3, -3],
[2, 2], [-3, -3]]]], [[3, 7, 1, 5, 2], [0 < v, And(-v < u,u < v), x < u^2-v^2-\
1, u^2-v^2-x-1 < y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0],
[-3, -3], [2, 2], [-1482911/1048576, -741455/524288]]]], [[3, 7, 1, 5, 3], [0
< v, And(-v < u,u < v), x < u^2-v^2-1, u^2-v^2-x-1 < y, And(-(-u^2+v^2+1)^(1/2
) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-3, -3], [2,
2], [0, 0]]]], [[3, 7, 1, 5, 4], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, u^2
-v^2-x-1 < y, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3, -\
3], [2, 2], [741455/524288, 1482911/1048576]]]], [[3, 7, 1, 5, 5], [0 < v, And
(-v < u,u < v), x < u^2-v^2-1, u^2-v^2-x-1 < y, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [0, 0], [-3, -3], [2, 2], [3, 3]]]], [[1, 4, 7, 2, 1],
[v < 0, u = -(v^2+1)^(1/2), 1 < x, y = -x, z < 0], [regular_chain, [[-1, -1],
[-1482911/1048576, -741455/524288], [2, 2], [-2, -2], [-1, -1]]]], [[1, 4, 7,
2, 2], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y = -x, z = 0], [regular_chain, [[-1
, -1], [-1482911/1048576, -741455/524288], [2, 2], [-2, -2], [0, 0]]]], [[1, 4
, 7, 2, 3], [v < 0, u = -(v^2+1)^(1/2), 1 < x, y = -x, 0 < z], [regular_chain,
[[-1, -1], [-1482911/1048576, -741455/524288], [2, 2], [-2, -2], [1, 1]]]], [[
1, 8, 4, 5, 1], [v < 0, u = -v, x = 1, 2 < y, z < -1], [regular_chain, [[-1, -\
1], [1, 1], [1, 1], [3, 3], [-2, -2]]]], [[1, 8, 4, 5, 2], [v < 0, u = -v, x =
1, 2 < y, z = -1], [regular_chain, [[-1, -1], [1, 1], [1, 1], [3, 3], [-1, -1]
]]], [[1, 8, 4, 5, 3], [v < 0, u = -v, x = 1, 2 < y, And(-1 < z,z < 1)], [
regular_chain, [[-1, -1], [1, 1], [1, 1], [3, 3], [0, 0]]]], [[1, 8, 4, 5, 4],
[v < 0, u = -v, x = 1, 2 < y, z = 1], [regular_chain, [[-1, -1], [1, 1], [1, 1
], [3, 3], [1, 1]]]], [[1, 8, 4, 5, 5], [v < 0, u = -v, x = 1, 2 < y, 1 < z],
[regular_chain, [[-1, -1], [1, 1], [1, 1], [3, 3], [2, 2]]]], [[2, 7, 2, 2, 1]
, [v = 0, And(0 < u,u < 1), x = -1, y = -u^2, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-1/4, -1/4], [-2, -2]]]], [[2,
7, 2, 2, 2], [v = 0, And(0 < u,u < 1), x = -1, y = -u^2, z = -(-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-1/4, -1/4], [-1816187/2097152
, -3632373/4194304]]]], [[2, 7, 2, 2, 3], [v = 0, And(0 < u,u < 1), x = -1, y
= -u^2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0],
[1/2, 1/2], [-1, -1], [-1/4, -1/4], [-1/8388608, -1/8388608]]]], [[2, 7, 2, 2,
4], [v = 0, And(0 < u,u < 1), x = -1, y = -u^2, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-1/4, -1/4], [908093/1048576, 
454047/524288]]]], [[2, 7, 2, 2, 5], [v = 0, And(0 < u,u < 1), x = -1, y = -u^
2, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-1/4,
-1/4], [2, 2]]]], [[2, 10, 4, 3, 1], [v = 0, u = 2^(1/2), x = 1, 0 < y, z = z]
, [regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [1, 1], [1, 1], [
0, 0]]]], [[1, 12, 2, 1, 1], [v < 0, u = (v^2+2)^(1/2), x = -1, y < -2, z = z]
, [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [-1, -1], [-3,
-3], [0, 0]]]], [[2, 3, 1, 4, 1], [v = 0, And(-2^(1/2) < u,u < -1), x < -1, y
= u^2-x-1, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/
1048576], [-2, -2], [1288231/524288, 2576463/1048576], [0, 0]]]], [[3, 3, 4, 1
, 1], [0 < v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = u^2-v^2-1, y < 0
, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [
248903/524288, 497807/1048576], [-1, -1], [0, 0]]]], [[3, 7, 1, 4, 1], [0 < v,
And(-v < u,u < v), x < u^2-v^2-1, y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-3, -3], [1, 1], [-3, -3]]]], [[3, 7, 1, 4, 2
], [0 < v, And(-v < u,u < v), x < u^2-v^2-1, y = u^2-v^2-x-1, z = -(-u^2+v^2+1
)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3, -3], [1, 1], [-1482911/1048576
, -741455/524288]]]], [[3, 7, 1, 4, 3], [0 < v, And(-v < u,u < v), x < u^2-v^2
-1, y = u^2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [-3, -3], [1, 1], [0, 0]]]], [[3, 7, 1, 4, 4],
[0 < v, And(-v < u,u < v), x < u^2-v^2-1, y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1
/2)], [regular_chain, [[1, 1], [0, 0], [-3, -3], [1, 1], [741455/524288, 
1482911/1048576]]]], [[3, 7, 1, 4, 5], [0 < v, And(-v < u,u < v), x < u^2-v^2-\
1, y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0],
[-3, -3], [1, 1], [3, 3]]]], [[1, 4, 6, 4, 1], [v < 0, u = -(v^2+1)^(1/2), x =
1, y = 1, z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288
], [1, 1], [1, 1], [-1, -1]]]], [[1, 4, 6, 4, 2], [v < 0, u = -(v^2+1)^(1/2),
x = 1, y = 1, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/
524288], [1, 1], [1, 1], [0, 0]]]], [[1, 4, 6, 4, 3], [v < 0, u = -(v^2+1)^(1/
2), x = 1, y = 1, 0 < z], [regular_chain, [[-1, -1], [-1482911/1048576, -\
741455/524288], [1, 1], [1, 1], [1, 1]]]], [[1, 8, 5, 1, 1], [v < 0, u = -v, 1
< x, y < -1-x, z < -1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [-4, -4], [
-2, -2]]]], [[1, 8, 5, 1, 2], [v < 0, u = -v, 1 < x, y < -1-x, z = -1], [
regular_chain, [[-1, -1], [1, 1], [2, 2], [-4, -4], [-1, -1]]]], [[1, 8, 5, 1,
3], [v < 0, u = -v, 1 < x, y < -1-x, And(-1 < z,z < 1)], [regular_chain, [[-1,
-1], [1, 1], [2, 2], [-4, -4], [0, 0]]]], [[1, 8, 5, 1, 4], [v < 0, u = -v, 1
< x, y < -1-x, z = 1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [-4, -4], [1
, 1]]]], [[1, 8, 5, 1, 5], [v < 0, u = -v, 1 < x, y < -1-x, 1 < z], [
regular_chain, [[-1, -1], [1, 1], [2, 2], [-4, -4], [2, 2]]]], [[2, 7, 2, 1, 1
], [v = 0, And(0 < u,u < 1), x = -1, y < -u^2, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-2, -2], [-2, -2]]]], [[2, 7, 2
, 1, 2], [v = 0, And(0 < u,u < 1), x = -1, y < -u^2, z = -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-2, -2], [-1816187/2097152, -\
3632373/4194304]]]], [[2, 7, 2, 1, 3], [v = 0, And(0 < u,u < 1), x = -1, y < -
u^2, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1
/2, 1/2], [-1, -1], [-2, -2], [-1/8388608, -1/8388608]]]], [[2, 7, 2, 1, 4], [
v = 0, And(0 < u,u < 1), x = -1, y < -u^2, z = (-u^2+1)^(1/2)], [regular_chain
, [[0, 0], [1/2, 1/2], [-1, -1], [-2, -2], [908093/1048576, 454047/524288]]]],
[[2, 7, 2, 1, 5], [v = 0, And(0 < u,u < 1), x = -1, y < -u^2, (-u^2+1)^(1/2) <
z], [regular_chain, [[0, 0], [1/2, 1/2], [-1, -1], [-2, -2], [2, 2]]]], [[2, 
10, 5, 3, 1], [v = 0, u = 2^(1/2), 1 < x, And(1-x < y,y < x-1), z = z], [
regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [2, 2], [0, 0], [0,
0]]]], [[1, 12, 1, 3, 1], [v < 0, u = (v^2+2)^(1/2), x < -1, And(x-1 < y,y < 1
-x), z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [-2,
-2], [0, 0], [0, 0]]]], [[2, 3, 1, 5, 1], [v = 0, And(-2^(1/2) < u,u < -1), x
< -1, u^2-x-1 < y, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -\
1265743/1048576], [-2, -2], [4, 4], [0, 0]]]], [[3, 3, 3, 5, 1], [0 < v, And(-
(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), u^2-v^2-x-1
< y, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-\
275385/1048576, -275385/1048576], [2, 2], [0, 0]]]], [[3, 7, 2, 2, 1], [0 < v,
And(-v < u,u < v), x = u^2-v^2-1, y = 0, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-2, -2], [0, 0], [-3, -3]]]], [[3, 7, 2, 2, 2
], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, y = 0, z = -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[1, 1], [0, 0], [-2, -2], [0, 0], [-1482911/1048576, -741455/
524288]]]], [[3, 7, 2, 2, 3], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, y = 0,
And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1],
[0, 0], [-2, -2], [0, 0], [0, 0]]]], [[3, 7, 2, 2, 4], [0 < v, And(-v < u,u <
v), x = u^2-v^2-1, y = 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0
, 0], [-2, -2], [0, 0], [741455/524288, 1482911/1048576]]]], [[3, 7, 2, 2, 5],
[0 < v, And(-v < u,u < v), x = u^2-v^2-1, y = 0, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [0, 0], [-2, -2], [0, 0], [3, 3]]]], [[1, 4, 6, 5, 1],
[v < 0, u = -(v^2+1)^(1/2), x = 1, 1 < y, z < 0], [regular_chain, [[-1, -1], [
-1482911/1048576, -741455/524288], [1, 1], [2, 2], [-1, -1]]]], [[1, 4, 6, 5,
2], [v < 0, u = -(v^2+1)^(1/2), x = 1, 1 < y, z = 0], [regular_chain, [[-1, -1
], [-1482911/1048576, -741455/524288], [1, 1], [2, 2], [0, 0]]]], [[1, 4, 6, 5
, 3], [v < 0, u = -(v^2+1)^(1/2), x = 1, 1 < y, 0 < z], [regular_chain, [[-1,
-1], [-1482911/1048576, -741455/524288], [1, 1], [2, 2], [1, 1]]]], [[1, 8, 5,
2, 1], [v < 0, u = -v, 1 < x, y = -1-x, z < -1], [regular_chain, [[-1, -1], [1
, 1], [2, 2], [-3, -3], [-2, -2]]]], [[1, 8, 5, 2, 2], [v < 0, u = -v, 1 < x,
y = -1-x, z = -1], [regular_chain, [[-1, -1], [1, 1], [2, 2], [-3, -3], [-1, -\
1]]]], [[1, 8, 5, 2, 3], [v < 0, u = -v, 1 < x, y = -1-x, And(-1 < z,z < 1)],
[regular_chain, [[-1, -1], [1, 1], [2, 2], [-3, -3], [0, 0]]]], [[1, 8, 5, 2,
4], [v < 0, u = -v, 1 < x, y = -1-x, z = 1], [regular_chain, [[-1, -1], [1, 1]
, [2, 2], [-3, -3], [1, 1]]]], [[1, 8, 5, 2, 5], [v < 0, u = -v, 1 < x, y = -1
-x, 1 < z], [regular_chain, [[-1, -1], [1, 1], [2, 2], [-3, -3], [2, 2]]]], [[
2, 7, 1, 5, 1], [v = 0, And(0 < u,u < 1), x < -1, u^2-x-1 < y, z < -(-u^2+1)^(
1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [3, 3], [-2, -2]]]], [[2
, 7, 1, 5, 2], [v = 0, And(0 < u,u < 1), x < -1, u^2-x-1 < y, z = -(-u^2+1)^(1
/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [3, 3], [-1816187/2097152
, -3632373/4194304]]]], [[2, 7, 1, 5, 3], [v = 0, And(0 < u,u < 1), x < -1, u^
2-x-1 < y, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0,
0], [1/2, 1/2], [-2, -2], [3, 3], [-1/8388608, -1/8388608]]]], [[2, 7, 1, 5, 4
], [v = 0, And(0 < u,u < 1), x < -1, u^2-x-1 < y, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [3, 3], [908093/1048576, 454047/
524288]]]], [[2, 7, 1, 5, 5], [v = 0, And(0 < u,u < 1), x < -1, u^2-x-1 < y, (
-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [3, 3], [2,
2]]]], [[2, 10, 5, 2, 1], [v = 0, u = 2^(1/2), 1 < x, y = 1-x, z = z], [
regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [2, 2], [-1, -1], [0
, 0]]]], [[1, 12, 1, 4, 1], [v < 0, u = (v^2+2)^(1/2), x < -1, y = 1-x, z = z]
, [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [-2, -2], [3, 3
], [0, 0]]]], [[2, 3, 2, 1, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = -1, y <
-u^2, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [
-1, -1], [-3, -3], [0, 0]]]], [[3, 3, 3, 4, 1], [0 < v, And(-(v^2+2)^(1/2) < u
,u < -(v^2+1)^(1/2)), And(-1 < x,x < u^2-v^2-1), y = u^2-v^2-x-1, z = z], [
regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [-275385/1048576
, -275385/1048576], [773191/1048576, 96649/131072], [0, 0]]]], [[3, 7, 2, 1, 1
], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, y < 0, z < -(-u^2+v^2+1)^(1/2)],
[regular_chain, [[1, 1], [0, 0], [-2, -2], [-1, -1], [-3, -3]]]], [[3, 7, 2, 1
, 2], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, y < 0, z = -(-u^2+v^2+1)^(1/2)
], [regular_chain, [[1, 1], [0, 0], [-2, -2], [-1, -1], [-1482911/1048576, -\
741455/524288]]]], [[3, 7, 2, 1, 3], [0 < v, And(-v < u,u < v), x = u^2-v^2-1,
y < 0, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [
[1, 1], [0, 0], [-2, -2], [-1, -1], [0, 0]]]], [[3, 7, 2, 1, 4], [0 < v, And(-
v < u,u < v), x = u^2-v^2-1, y < 0, z = (-u^2+v^2+1)^(1/2)], [regular_chain, [
[1, 1], [0, 0], [-2, -2], [-1, -1], [741455/524288, 1482911/1048576]]]], [[3,
7, 2, 1, 5], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, y < 0, (-u^2+v^2+1)^(1/
2) < z], [regular_chain, [[1, 1], [0, 0], [-2, -2], [-1, -1], [3, 3]]]], [[1,
12, 2, 4, 1], [v < 0, u = (v^2+2)^(1/2), x = -1, y = 2, z = z], [regular_chain
, [[-1, -1], [908093/524288, 1816187/1048576], [-1, -1], [2, 2], [0, 0]]]], [[
2, 3, 2, 2, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = -1, y = -u^2, z = z], [
regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [-1, -1], [-\
1527887/1048576, -763943/524288], [0, 0]]]], [[3, 3, 5, 3, 1], [0 < v, And(-(v
^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), And(u^2-v^2-x-1
< y,y < x-u^2+v^2+1), z = z], [regular_chain, [[1, 1], [-6598195/4194304, -\
6598195/4194304], [1546383/2097152, 1546383/2097152], [0, 0], [0, 0]]]], [[3,
7, 3, 1, 1], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y < u^2-v^2
-x-1, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2],
[-2, -2], [-3, -3]]]], [[3, 7, 3, 1, 2], [0 < v, And(-v < u,u < v), And(u^2-v^
2-1 < x,x < -1), y < u^2-v^2-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[
1, 1], [0, 0], [-3/2, -3/2], [-2, -2], [-1482911/1048576, -741455/524288]]]],
[[3, 7, 3, 1, 3], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y < u^
2-v^2-x-1, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [
regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [-2, -2], [0, 0]]]], [[3, 7, 3,
1, 4], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y < u^2-v^2-x-1,
z = (-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [-2, -\
2], [741455/524288, 1482911/1048576]]]], [[3, 7, 3, 1, 5], [0 < v, And(-v < u,
u < v), And(u^2-v^2-1 < x,x < -1), y < u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [
regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [-2, -2], [3, 3]]]], [[1, 4, 6,
2, 1], [v < 0, u = -(v^2+1)^(1/2), x = 1, y = -1, z < 0], [regular_chain, [[-1
, -1], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1], [-1, -1]]]], [[1,
4, 6, 2, 2], [v < 0, u = -(v^2+1)^(1/2), x = 1, y = -1, z = 0], [regular_chain
, [[-1, -1], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1], [0, 0]]]],
[[1, 4, 6, 2, 3], [v < 0, u = -(v^2+1)^(1/2), x = 1, y = -1, 0 < z], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1, 1], [-1, -1]
, [1, 1]]]], [[1, 8, 3, 5, 1], [v < 0, u = -v, And(-1 < x,x < 1), x+1 < y, z <
-1], [regular_chain, [[-1, -1], [1, 1], [0, 0], [2, 2], [-2, -2]]]], [[1, 8, 3
, 5, 2], [v < 0, u = -v, And(-1 < x,x < 1), x+1 < y, z = -1], [regular_chain,
[[-1, -1], [1, 1], [0, 0], [2, 2], [-1, -1]]]], [[1, 8, 3, 5, 3], [v < 0, u =
-v, And(-1 < x,x < 1), x+1 < y, And(-1 < z,z < 1)], [regular_chain, [[-1, -1],
[1, 1], [0, 0], [2, 2], [0, 0]]]], [[1, 8, 3, 5, 4], [v < 0, u = -v, And(-1 <
x,x < 1), x+1 < y, z = 1], [regular_chain, [[-1, -1], [1, 1], [0, 0], [2, 2],
[1, 1]]]], [[1, 8, 3, 5, 5], [v < 0, u = -v, And(-1 < x,x < 1), x+1 < y, 1 < z
], [regular_chain, [[-1, -1], [1, 1], [0, 0], [2, 2], [2, 2]]]], [[2, 7, 1, 4,
1], [v = 0, And(0 < u,u < 1), x < -1, y = u^2-x-1, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [5/4, 5/4], [-2, -2]]]], [[2, 7,
1, 4, 2], [v = 0, And(0 < u,u < 1), x < -1, y = u^2-x-1, z = -(-u^2+1)^(1/2)],
[regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [5/4, 5/4], [-1816187/2097152,
-3632373/4194304]]]], [[2, 7, 1, 4, 3], [v = 0, And(0 < u,u < 1), x < -1, y =
u^2-x-1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain, [[0, 0]
, [1/2, 1/2], [-2, -2], [5/4, 5/4], [-1/8388608, -1/8388608]]]], [[2, 7, 1, 4,
4], [v = 0, And(0 < u,u < 1), x < -1, y = u^2-x-1, z = (-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [5/4, 5/4], [908093/1048576, 
454047/524288]]]], [[2, 7, 1, 4, 5], [v = 0, And(0 < u,u < 1), x < -1, y = u^2
-x-1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [5/4
, 5/4], [2, 2]]]], [[2, 10, 3, 5, 1], [v = 0, u = 2^(1/2), And(-1 < x,x < 1),
1-x < y, z = z], [regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [0
, 0], [2, 2], [0, 0]]]], [[1, 12, 2, 5, 1], [v < 0, u = (v^2+2)^(1/2), x = -1,
2 < y, z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [-\
1, -1], [3, 3], [0, 0]]]], [[2, 3, 2, 3, 1], [v = 0, And(-2^(1/2) < u,u < -1),
x = -1, And(-u^2 < y,y < u^2), z = z], [regular_chain, [[0, 0], [-1265743/
1048576, -1265743/1048576], [-1, -1], [0, 0], [0, 0]]]], [[3, 3, 5, 2, 1], [0
< v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y =
u^2-v^2-x-1, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/
4194304], [1546383/2097152, 1546383/2097152], [-137693/524288, -275385/1048576
], [0, 0]]]], [[3, 7, 2, 3, 1], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, 0 <
y, z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-2, -2], [1, 1]
, [-3, -3]]]], [[3, 7, 2, 3, 2], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, 0 <
y, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-2, -2], [1, 1]
, [-1482911/1048576, -741455/524288]]]], [[3, 7, 2, 3, 3], [0 < v, And(-v < u,
u < v), x = u^2-v^2-1, 0 < y, And(-(-u^2+v^2+1)^(1/2) < z,z < (-u^2+v^2+1)^(1/
2))], [regular_chain, [[1, 1], [0, 0], [-2, -2], [1, 1], [0, 0]]]], [[3, 7, 2,
3, 4], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, 0 < y, z = (-u^2+v^2+1)^(1/2)
], [regular_chain, [[1, 1], [0, 0], [-2, -2], [1, 1], [741455/524288, 1482911/
1048576]]]], [[3, 7, 2, 3, 5], [0 < v, And(-v < u,u < v), x = u^2-v^2-1, 0 < y
, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1, 1], [0, 0], [-2, -2], [1, 1],
[3, 3]]]], [[1, 4, 6, 3, 1], [v < 0, u = -(v^2+1)^(1/2), x = 1, And(-1 < y,y <
1), z < 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1,
1], [0, 0], [-1, -1]]]], [[1, 4, 6, 3, 2], [v < 0, u = -(v^2+1)^(1/2), x = 1,
And(-1 < y,y < 1), z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -\
741455/524288], [1, 1], [0, 0], [0, 0]]]], [[1, 4, 6, 3, 3], [v < 0, u = -(v^2
+1)^(1/2), x = 1, And(-1 < y,y < 1), 0 < z], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [1, 1], [0, 0], [1, 1]]]], [[1, 8, 4, 1, 1],
[v < 0, u = -v, x = 1, y < -2, z < -1], [regular_chain, [[-1, -1], [1, 1], [1,
1], [-3, -3], [-2, -2]]]], [[1, 8, 4, 1, 2], [v < 0, u = -v, x = 1, y < -2, z
= -1], [regular_chain, [[-1, -1], [1, 1], [1, 1], [-3, -3], [-1, -1]]]], [[1,
8, 4, 1, 3], [v < 0, u = -v, x = 1, y < -2, And(-1 < z,z < 1)], [regular_chain
, [[-1, -1], [1, 1], [1, 1], [-3, -3], [0, 0]]]], [[1, 8, 4, 1, 4], [v < 0, u
= -v, x = 1, y < -2, z = 1], [regular_chain, [[-1, -1], [1, 1], [1, 1], [-3, -\
3], [1, 1]]]], [[1, 8, 4, 1, 5], [v < 0, u = -v, x = 1, y < -2, 1 < z], [
regular_chain, [[-1, -1], [1, 1], [1, 1], [-3, -3], [2, 2]]]], [[2, 7, 1, 3, 1
], [v = 0, And(0 < u,u < 1), x < -1, And(x-u^2+1 < y,y < u^2-x-1), z < -(-u^2+
1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [0, 0], [-2, -2]]]],
[[2, 7, 1, 3, 2], [v = 0, And(0 < u,u < 1), x < -1, And(x-u^2+1 < y,y < u^2-x-\
1), z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [0, 0
], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 1, 3, 3], [v = 0, And(0 <
u,u < 1), x < -1, And(x-u^2+1 < y,y < u^2-x-1), And(-(-u^2+1)^(1/2) < z,z < (-
u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [0, 0], [-1/
8388608, -1/8388608]]]], [[2, 7, 1, 3, 4], [v = 0, And(0 < u,u < 1), x < -1, 
And(x-u^2+1 < y,y < u^2-x-1), z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1
/2, 1/2], [-2, -2], [0, 0], [908093/1048576, 454047/524288]]]], [[2, 7, 1, 3,
5], [v = 0, And(0 < u,u < 1), x < -1, And(x-u^2+1 < y,y < u^2-x-1), (-u^2+1)^(
1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [0, 0], [2, 2]]]], [
[2, 10, 3, 4, 1], [v = 0, u = 2^(1/2), And(-1 < x,x < 1), y = 1-x, z = z], [
regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [0, 0], [1, 1], [0,
0]]]], [[1, 12, 2, 2, 1], [v < 0, u = (v^2+2)^(1/2), x = -1, y = -2, z = z], [
regular_chain, [[-1, -1], [908093/524288, 1816187/1048576], [-1, -1], [-2, -2]
, [0, 0]]]], [[2, 3, 2, 4, 1], [v = 0, And(-2^(1/2) < u,u < -1), x = -1, y = u
^2, z = z], [regular_chain, [[0, 0], [-1265743/1048576, -1265743/1048576], [-1
, -1], [763943/524288, 1527887/1048576], [0, 0]]]], [[3, 3, 5, 1, 1], [0 < v,
And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), And(u^2-v^2-1 < x,x < 1), y < u^2-
v^2-x-1, z = z], [regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304]
, [1546383/2097152, 1546383/2097152], [-2, -2], [0, 0]]]], [[3, 7, 3, 3, 1], [
0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1 < y,y < x
-u^2+v^2+1), z < -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2,
-3/2], [0, 0], [-3, -3]]]], [[3, 7, 3, 3, 2], [0 < v, And(-v < u,u < v), And(u
^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = -(-u^2+v^2+1)^
(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [0, 0], [-1482911/
1048576, -741455/524288]]]], [[3, 7, 3, 3, 3], [0 < v, And(-v < u,u < v), And(
u^2-v^2-1 < x,x < -1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), And(-(-u^2+v^2+1)
^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-3/2, -\
3/2], [0, 0], [0, 0]]]], [[3, 7, 3, 3, 4], [0 < v, And(-v < u,u < v), And(u^2-
v^2-1 < x,x < -1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), z = (-u^2+v^2+1)^(1/2
)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [0, 0], [741455/524288, 
1482911/1048576]]]], [[3, 7, 3, 3, 5], [0 < v, And(-v < u,u < v), And(u^2-v^2-\
1 < x,x < -1), And(u^2-v^2-x-1 < y,y < x-u^2+v^2+1), (-u^2+v^2+1)^(1/2) < z],
[regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [0, 0], [3, 3]]]], [[1, 4, 5, 5
, 1], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1), x < y, z < 0], [
regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288], [1/2, 1/2], [2,
2], [-1, -1]]]], [[1, 4, 5, 5, 2], [v < 0, u = -(v^2+1)^(1/2), And(0 < x,x < 1
), x < y, z = 0], [regular_chain, [[-1, -1], [-1482911/1048576, -741455/524288
], [1/2, 1/2], [2, 2], [0, 0]]]], [[1, 4, 5, 5, 3], [v < 0, u = -(v^2+1)^(1/2)
, And(0 < x,x < 1), x < y, 0 < z], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [1/2, 1/2], [2, 2], [1, 1]]]], [[1, 8, 4, 2, 1], [v
< 0, u = -v, x = 1, y = -2, z < -1], [regular_chain, [[-1, -1], [1, 1], [1, 1]
, [-2, -2], [-2, -2]]]], [[1, 8, 4, 2, 2], [v < 0, u = -v, x = 1, y = -2, z =
-1], [regular_chain, [[-1, -1], [1, 1], [1, 1], [-2, -2], [-1, -1]]]], [[1, 8,
4, 2, 3], [v < 0, u = -v, x = 1, y = -2, And(-1 < z,z < 1)], [regular_chain, [
[-1, -1], [1, 1], [1, 1], [-2, -2], [0, 0]]]], [[1, 8, 4, 2, 4], [v < 0, u = -
v, x = 1, y = -2, z = 1], [regular_chain, [[-1, -1], [1, 1], [1, 1], [-2, -2],
[1, 1]]]], [[1, 8, 4, 2, 5], [v < 0, u = -v, x = 1, y = -2, 1 < z], [
regular_chain, [[-1, -1], [1, 1], [1, 1], [-2, -2], [2, 2]]]], [[2, 7, 1, 2, 1
], [v = 0, And(0 < u,u < 1), x < -1, y = x-u^2+1, z < -(-u^2+1)^(1/2)], [
regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [-5/4, -5/4], [-2, -2]]]], [[2,
7, 1, 2, 2], [v = 0, And(0 < u,u < 1), x < -1, y = x-u^2+1, z = -(-u^2+1)^(1/2
)], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [-5/4, -5/4], [-1816187/
2097152, -3632373/4194304]]]], [[2, 7, 1, 2, 3], [v = 0, And(0 < u,u < 1), x <
-1, y = x-u^2+1, And(-(-u^2+1)^(1/2) < z,z < (-u^2+1)^(1/2))], [regular_chain,
[[0, 0], [1/2, 1/2], [-2, -2], [-5/4, -5/4], [-1/8388608, -1/8388608]]]], [[2,
7, 1, 2, 4], [v = 0, And(0 < u,u < 1), x < -1, y = x-u^2+1, z = (-u^2+1)^(1/2)
], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [-5/4, -5/4], [908093/
1048576, 454047/524288]]]], [[2, 7, 1, 2, 5], [v = 0, And(0 < u,u < 1), x < -1
, y = x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0, 0], [1/2, 1/2], [-2,
-2], [-5/4, -5/4], [2, 2]]]], [[2, 10, 4, 2, 1], [v = 0, u = 2^(1/2), x = 1, y
= 0, z = z], [regular_chain, [[0, 0], [741455/524288, 1482911/1048576], [1, 1]
, [0, 0], [0, 0]]]], [[1, 12, 2, 3, 1], [v < 0, u = (v^2+2)^(1/2), x = -1, And
(-2 < y,y < 2), z = z], [regular_chain, [[-1, -1], [908093/524288, 1816187/
1048576], [-1, -1], [0, 0], [0, 0]]]], [[2, 3, 2, 5, 1], [v = 0, And(-2^(1/2)
< u,u < -1), x = -1, u^2 < y, z = z], [regular_chain, [[0, 0], [-1265743/
1048576, -1265743/1048576], [-1, -1], [3, 3], [0, 0]]]], [[3, 3, 4, 3, 1], [0
< v, And(-(v^2+2)^(1/2) < u,u < -(v^2+1)^(1/2)), x = u^2-v^2-1, 0 < y, z = z],
[regular_chain, [[1, 1], [-6598195/4194304, -6598195/4194304], [248903/524288,
497807/1048576], [1, 1], [0, 0]]]], [[3, 7, 3, 2, 1], [0 < v, And(-v < u,u < v
), And(u^2-v^2-1 < x,x < -1), y = u^2-v^2-x-1, z < -(-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [-1/2, -1/2], [-3, -3]]]], [[3,
7, 3, 2, 2], [0 < v, And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y = u^2-v^2
-x-1, z = -(-u^2+v^2+1)^(1/2)], [regular_chain, [[1, 1], [0, 0], [-3/2, -3/2],
[-1/2, -1/2], [-1482911/1048576, -741455/524288]]]], [[3, 7, 3, 2, 3], [0 < v,
And(-v < u,u < v), And(u^2-v^2-1 < x,x < -1), y = u^2-v^2-x-1, And(-(-u^2+v^2+
1)^(1/2) < z,z < (-u^2+v^2+1)^(1/2))], [regular_chain, [[1, 1], [0, 0], [-3/2,
-3/2], [-1/2, -1/2], [0, 0]]]], [[3, 7, 3, 2, 4], [0 < v, And(-v < u,u < v), 
And(u^2-v^2-1 < x,x < -1), y = u^2-v^2-x-1, z = (-u^2+v^2+1)^(1/2)], [
regular_chain, [[1, 1], [0, 0], [-3/2, -3/2], [-1/2, -1/2], [741455/524288, 
1482911/1048576]]]], [[3, 7, 3, 2, 5], [0 < v, And(-v < u,u < v), And(u^2-v^2-\
1 < x,x < -1), y = u^2-v^2-x-1, (-u^2+v^2+1)^(1/2) < z], [regular_chain, [[1,
1], [0, 0], [-3/2, -3/2], [-1/2, -1/2], [3, 3]]]], [[1, 4, 6, 1, 1], [v < 0, u
= -(v^2+1)^(1/2), x = 1, y < -1, z < 0], [regular_chain, [[-1, -1], [-1482911/
1048576, -741455/524288], [1, 1], [-2, -2], [-1, -1]]]], [[1, 4, 6, 1, 2], [v
< 0, u = -(v^2+1)^(1/2), x = 1, y < -1, z = 0], [regular_chain, [[-1, -1], [-\
1482911/1048576, -741455/524288], [1, 1], [-2, -2], [0, 0]]]], [[1, 4, 6, 1, 3
], [v < 0, u = -(v^2+1)^(1/2), x = 1, y < -1, 0 < z], [regular_chain, [[-1, -1
], [-1482911/1048576, -741455/524288], [1, 1], [-2, -2], [1, 1]]]], [[1, 8, 4,
3, 1], [v < 0, u = -v, x = 1, And(-2 < y,y < 2), z < -1], [regular_chain, [[-1
, -1], [1, 1], [1, 1], [0, 0], [-2, -2]]]], [[1, 8, 4, 3, 2], [v < 0, u = -v,
x = 1, And(-2 < y,y < 2), z = -1], [regular_chain, [[-1, -1], [1, 1], [1, 1],
[0, 0], [-1, -1]]]], [[1, 8, 4, 3, 3], [v < 0, u = -v, x = 1, And(-2 < y,y < 2
), And(-1 < z,z < 1)], [regular_chain, [[-1, -1], [1, 1], [1, 1], [0, 0], [0,
0]]]], [[1, 8, 4, 3, 4], [v < 0, u = -v, x = 1, And(-2 < y,y < 2), z = 1], [
regular_chain, [[-1, -1], [1, 1], [1, 1], [0, 0], [1, 1]]]], [[1, 8, 4, 3, 5],
[v < 0, u = -v, x = 1, And(-2 < y,y < 2), 1 < z], [regular_chain, [[-1, -1], [
1, 1], [1, 1], [0, 0], [2, 2]]]], [[2, 7, 1, 1, 1], [v = 0, And(0 < u,u < 1),
x < -1, y < x-u^2+1, z < -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2]
, [-2, -2], [-3, -3], [-2, -2]]]], [[2, 7, 1, 1, 2], [v = 0, And(0 < u,u < 1),
x < -1, y < x-u^2+1, z = -(-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2]
, [-2, -2], [-3, -3], [-1816187/2097152, -3632373/4194304]]]], [[2, 7, 1, 1, 3
], [v = 0, And(0 < u,u < 1), x < -1, y < x-u^2+1, And(-(-u^2+1)^(1/2) < z,z <
(-u^2+1)^(1/2))], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2], [-3, -3], [-1
/8388608, -1/8388608]]]], [[2, 7, 1, 1, 4], [v = 0, And(0 < u,u < 1), x < -1,
y < x-u^2+1, z = (-u^2+1)^(1/2)], [regular_chain, [[0, 0], [1/2, 1/2], [-2, -2
], [-3, -3], [908093/1048576, 454047/524288]]]], [[2, 7, 1, 1, 5], [v = 0, And
(0 < u,u < 1), x < -1, y < x-u^2+1, (-u^2+1)^(1/2) < z], [regular_chain, [[0,
0], [1/2, 1/2], [-2, -2], [-3, -3], [2, 2]]]], [[2, 10, 4, 1, 1], [v = 0, u =
2^(1/2), x = 1, y < 0, z = z], [regular_chain, [[0, 0], [741455/524288, 
1482911/1048576], [1, 1], [-1, -1], [0, 0]]]]];
