from libsolve import Permutation
from itertools import permutations

PRINT_LATEX = False

# (1 2 5 8 3 7 6)(4)
rhs = Permutation([1, 4, 6, 3, 7, 0, 5, 2])

# (2 8 5 7 3 6 4)(1)
lhs = Permutation([0, 7, 5, 1, 6, 3, 2, 4])

for perm in permutations(range(8), 8):
    p = Permutation(perm)

    id = list(range(8))
    right = rhs.apply(id)
    left = p.apply(lhs.apply(p.apply(id)))
    if left == right:
        if PRINT_LATEX:
            print('\\begin{pmatrix}', end='')
            print(*range(1, 9), sep=' & ', end='')
            print(*map(lambda i: f'{i + 1}', p.perm),
                  sep=' & ',
                  end='\\end{pmatrix}\\\\\n')
        else:
            print(p.perm)