sints_in = (((-1, 2, 0, 2, 2, 0), (0, 0, 0), (0, 0, 0)), ((-1, 2, 0, 3, 1, 0), \
(0, 0, 0), (0, 0, 0)), ((0, 1, 0, 2, 2, 0), (0, 0, 0), (0, 0, 0)), \
((0, 1, 0, 3, 1, 0), (0, 0, 0), (0, 0, 0)), ((0, 2, 0, 1, 2, 0), (0, \
0, 0), (0, 0, 0)), ((0, 2, 0, 2, 1, 0), (0, 0, 0), (0, 0, 0)), ((0, \
2, 0, 2, 2, 0), (1, 0, 1), (0, 0, 0)), ((0, 2, 0, 2, 2, 0), (2, 0, \
0), (0, 0, 0)), ((0, 3, 0, 2, 1, 0), (1, 1, 0), (0, 0, 0)), ((1, 0, \
0, 2, 2, 0), (0, 0, 0), (0, 0, 0)), ((1, 0, 0, 3, 1, 0), (0, 0, 0), \
(0, 0, 0)), ((1, 1, 0, 1, 2, 0), (0, 0, 0), (0, 0, 0)), ((1, 1, 0, 1, \
2, 1), (1, 0, 1), (0, 0, 0)), ((1, 1, 0, 1, 2, 1), (2, 0, 0), (0, 0, \
0)), ((1, 1, 0, 2, 1, 0), (0, 0, 0), (0, 0, 0)), ((1, 1, 0, 2, 1, 1), \
(1, 0, 1), (0, 0, 0)), ((1, 1, 0, 2, 1, 1), (2, 0, 0), (0, 0, 0)), \
((1, 1, 0, 2, 2, 0), (1, 0, 1), (0, 0, 0)), ((1, 1, 0, 2, 2, 0), (2, \
0, 0), (0, 0, 0)), ((1, 1, 1, 1, 1, 0), (0, 0, 0), (0, 0, 0)), ((1, \
2, 0, 0, 2, 0), (0, 0, 0), (0, 0, 0)), ((1, 2, 0, 1, 1, 0), (0, 0, \
0), (0, 0, 0)), ((1, 2, 0, 1, 2, 0), (1, 0, 1), (0, 0, 0)), ((1, 2, \
0, 1, 2, 0), (2, 0, 0), (0, 0, 0)), ((1, 2, 0, 2, 1, 0), (0, 2, 0), \
(0, 0, 0)), ((1, 2, 0, 2, 1, 0), (1, 1, 0), (0, 0, 0)), ((1, 2, 0, 2, \
1, 0), (2, 0, 0), (0, 0, 0)), ((1, 2, 1, 1, 0, 1), (1, 1, 0), (0, 0, \
0)), ((1, 3, 0, 1, 1, 0), (1, 1, 0), (0, 0, 0)), ((2, 0, 0, 1, 2, 1), \
(1, 0, 1), (0, 0, 0)), ((2, 0, 0, 1, 2, 1), (2, 0, 0), (0, 0, 0)), \
((2, 0, 0, 2, 1, 0), (0, 0, 0), (0, 0, 0)), ((2, 0, 0, 2, 1, 1), (1, \
0, 1), (0, 0, 0)), ((2, 0, 0, 2, 1, 1), (2, 0, 0), (0, 0, 0)), ((2, \
0, 0, 2, 2, 0), (1, 0, 1), (0, 0, 0)), ((2, 0, 0, 2, 2, 0), (2, 0, \
0), (0, 0, 0)), ((2, 0, 2, 0, 0, 2), (1, 1, 0), (0, 0, 0)), ((2, 1, \
-1, 1, 2, 1), (1, 0, 1), (0, 0, 0)), ((2, 1, -1, 1, 2, 1), (2, 0, 0), \
(0, 0, 0)), ((2, 1, 0, 0, 2, 1), (1, 0, 1), (0, 0, 0)), ((2, 1, 0, 0, \
2, 1), (2, 0, 0), (0, 0, 0)), ((2, 1, 0, 1, 1, 0), (0, 0, 0), (0, 0, \
0)), ((2, 1, 0, 1, 1, 1), (1, 0, 1), (0, 0, 0)), ((2, 1, 0, 1, 1, 1), \
(2, 0, 0), (0, 0, 0)), ((2, 1, 0, 1, 2, 0), (1, 0, 1), (0, 0, 0)), \
((2, 1, 0, 1, 2, 0), (2, 0, 0), (0, 0, 0)), ((2, 1, 0, 2, 1, 0), (1, \
1, 0), (0, 0, 0)), ((2, 1, 0, 2, 1, 0), (2, 0, 0), (0, 0, 0)), ((2, \
1, 1, 0, 0, 2), (1, 1, 0), (0, 0, 0)), ((2, 1, 1, 1, 0, 1), (1, 1, \
0), (0, 0, 0)), ((2, 1, 1, 1, 0, 1), (2, 0, 0), (0, 0, 0)), ((2, 1, \
1, 1, 1, 0), (2, 0, 0), (0, 0, 0)), ((2, 1, 2, 0, 0, 1), (1, 1, 0), \
(0, 0, 0)), ((2, 2, 0, 0, 0, 2), (1, 1, 0), (0, 0, 0)), ((2, 2, 0, 0, \
1, 0), (0, 0, 0), (0, 0, 0)), ((2, 2, 0, 0, 2, 0), (1, 0, 1), (0, 0, \
0)), ((2, 2, 0, 0, 2, 0), (2, 0, 0), (0, 0, 0)), ((2, 2, 0, 1, 1, 0), \
(1, 1, 0), (0, 0, 0)), ((2, 2, 0, 1, 1, 0), (2, 0, 0), (0, 0, 0)), \
((2, 2, 1, 0, 0, 0), (0, 0, 0), (0, 0, 0)), ((2, 2, 1, 0, 0, 1), (1, \
1, 0), (0, 0, 0)), ((2, 2, 2, 0, 0, 0), (1, 1, 0), (0, 0, 0)), ((2, \
3, 0, 0, 1, 0), (1, 1, 0), (0, 0, 0)), ((3, -1, 2, 0, 0, 2), (2, 0, \
0), (0, 0, 0)), ((3, 0, 0, 2, 1, 0), (1, 1, 0), (0, 0, 0)), ((3, 0, \
0, 2, 1, 0), (2, 0, 0), (0, 0, 0)), ((3, 0, 1, 0, 0, 2), (2, 0, 0), \
(0, 0, 0)), ((3, 0, 2, 0, 0, 1), (2, 0, 0), (0, 0, 0)), ((3, 1, 0, 0, \
0, 2), (2, 0, 0), (0, 0, 0)), ((3, 1, 0, 1, 1, 0), (1, 1, 0), (0, 0, \
0)), ((3, 1, 0, 1, 1, 0), (2, 0, 0), (0, 0, 0)), ((3, 1, 1, 0, 0, 0), \
(0, 0, 0), (0, 0, 0)), ((3, 1, 1, 0, 0, 1), (2, 0, 0), (0, 0, 0)), \
((3, 1, 2, 0, 0, 0), (2, 0, 0), (0, 0, 0)), ((3, 2, 0, 0, 1, 0), (1, \
1, 0), (0, 0, 0)), ((3, 2, 0, 0, 1, 0), (2, 0, 0), (0, 0, 0)), ((3, \
2, 1, 0, 0, 0), (2, 0, 0), (0, 0, 0)), ((4, -1, 0, 2, 1, 0), (2, 0, \
0), (0, 0, 0)), ((4, 1, 0, 0, 1, 0), (2, 0, 0), (0, 0, 0)), ((4, 1, \
1, 0, 0, 0), (2, 0, 0), (0, 0, 0)), ((4, 2, 0, -1, 1, 0), (2, 0, 0), \
(0, 0, 0)))

coeffs_in = [8 - 8*xi, 16 - 16*xi, -16, -32, -16 + 16*xi, -24 + 32*xi, 16 - \
16*xi, -16 + 16*xi, -32 + 32*xi, 8, 16, -16, -64, 64, -16, 64 - \
64*xi, -64 + 64*xi, -96 + 96*xi, 96 - 96*xi, 16, 8 - 8*xi, -16*xi, \
-32, 32, -32 + 32*xi, 96 - 96*xi, -32 + 32*xi, 64 - 64*xi, 64, -64, \
64, 8 - 8*xi, -64 + 64*xi, 64 - 64*xi, 80 - 80*xi, -80 + 80*xi, -16 + \
16*xi, 128, -128, 64, -64, -16 + 16*xi, -64, 64, -96, 96, -32 + \
96*xi, 32 - 160*xi, 32 - 32*xi, 64, -128, -16 + 16*xi, 32, -16 + \
16*xi, 8 - 8*xi, 16, -16, 64 + 64*xi, 64*xi, 8*d + 8*xi, -32 + 64*xi, \
-16, -32, -32 + 32*xi, 96 - 96*xi, -96 + 96*xi, 64, 64 - 64*xi, -32, \
-64, 128, 16*d + 16*xi, 64, -32 + 32*xi, -32, 96 - 128*xi, -32*d - \
32*xi, -32 + 32*xi, 96, -96*d - 96*xi, -64 + 64*xi]