import itertools


def check_854(magma):
    for (x, y, z) in itertools.product(range(len(magma)), repeat=3):
        if not x == magma[x][magma[magma[y][z]][magma[x][z]]]:
            return False
    return True


four_elem_magmas = [[[0, 0, 0, 0], [1, 0, 0, 0], [2, 0, 0, 0], [3, 0, 0, 0]],[[0, 0, 0, 0], [1, 0, 3, 2], [2, 0, 0, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 0, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 0, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 0, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 0, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 0, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 0, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 0, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 1, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 2, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 2, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 2, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 2, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 3, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 0, 0], [3, 2, 1, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 0, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 0, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 0, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 0, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 2, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 0], [2, 2, 2, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 2, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 2], [2, 2, 2, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 0], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 0], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 1], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 1], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 0], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 0], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 1], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 1], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 0], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 0], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 1], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 1], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 0], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 0], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 1], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 1], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 3, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 0, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 3, 0, 1], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 3, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 3, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 0, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 3, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 3, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 0, 3, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 0], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 0], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 1], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 1], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 0], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 0], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 1], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 1], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 1], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 1], [3, 3, 0, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 1], [3, 3, 1, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 1], [3, 3, 1, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 3, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 0, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 0, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 0, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 0, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 2, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 2, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 2, 2], [3, 0, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 2, 2], [3, 0, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 0, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 0, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 0, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 0, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 2, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 0], [2, 2, 2, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 2, 2], [3, 2, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 2], [2, 2, 2, 2], [3, 2, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 0], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 1]],[[0, 0, 0, 0], [1, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 0, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 0, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 0, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 0, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 0, 0], [3, 3, 0, 0]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 3, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 3, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 0, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 3, 0, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 3, 3, 2], [3, 3, 3, 0]],[[0, 0, 0, 0], [1, 3, 3, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[1, 0, 1, 1], [1, 1, 1, 1], [1, 2, 1, 1], [1, 3, 1, 1]],[[1, 0, 3, 2], [1, 1, 1, 1], [1, 2, 1, 2], [1, 3, 3, 1]],[[1, 0, 1, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 0]],[[1, 0, 1, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 1]],[[1, 0, 1, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 2]],[[1, 0, 1, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[1, 0, 1, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 1]],[[1, 0, 1, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[1, 0, 3, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 1]],[[1, 0, 3, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[1, 0, 3, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 1]],[[1, 0, 3, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[1, 0, 1, 0], [1, 3, 1, 1], [1, 2, 1, 2], [3, 3, 3, 0]],[[1, 0, 1, 0], [1, 3, 1, 1], [1, 2, 1, 2], [3, 3, 3, 2]],[[1, 0, 1, 0], [1, 3, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[1, 0, 1, 0], [1, 3, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[1, 0, 3, 0], [1, 3, 1, 1], [1, 2, 1, 2], [3, 3, 3, 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2]],[[2, 2, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[2, 2, 0, 0], [3, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[2, 2, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[2, 2, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[2, 2, 0, 0], [3, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[2, 3, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[2, 3, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[2, 3, 0, 0], [3, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[2, 3, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[2, 3, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[2, 3, 0, 0], [3, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 1]],[[3, 0, 1, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 1, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 1]],[[3, 0, 3, 0], [1, 1, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 3, 0], [1, 1, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 3, 3, 1], [1, 0, 3, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 3, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 3, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 3, 1, 1], [1, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 3, 1, 1], [1, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 0, 0, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 0, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 3, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 3, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 1], [3, 3, 1, 1]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 0, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 0, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 0, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 3, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 0, 3, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 1], [3, 3, 1, 1]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 1, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 2, 1, 2], [2, 2, 0, 2], [3, 2, 3, 2]],[[3, 0, 0, 0], [1, 2, 1, 2], [2, 2, 2, 2], [3, 2, 3, 2]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 0, 0], [1, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 0, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 0, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 3, 1], [2, 0, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 3, 1], [2, 0, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 0, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 0, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 3, 1], [2, 3, 0, 2], [3, 3, 3, 3]],[[3, 0, 0, 0], [1, 3, 3, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 0, 1, 1], [3, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 3, 0], [1, 0, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 1, 1, 1], [3, 2, 1, 2], [3, 3, 3, 1]],[[3, 0, 1, 0], [1, 1, 1, 1], [3, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 1, 1, 1], [3, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 1, 0], [1, 1, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 1, 1, 1], [3, 2, 1, 2], [3, 3, 3, 1]],[[3, 0, 3, 0], [1, 1, 1, 1], [3, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 1, 1, 1], [3, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 3, 0], [1, 1, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 2, 1, 1], [3, 2, 3, 2], [3, 3, 3, 1]],[[3, 0, 3, 0], [1, 2, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 3, 1, 1], [3, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 1, 0], [1, 3, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 3, 1, 1], [3, 2, 1, 2], [3, 3, 3, 3]],[[3, 0, 3, 0], [1, 3, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [2, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 2, 0, 0], [2, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [2, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [2, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 2, 0, 0], [2, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [2, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [2, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 3, 0, 0], [2, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [2, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [2, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 3, 0, 0], [2, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [2, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [2, 3, 0, 1], [2, 3, 3, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 2, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [3, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 2, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 2, 0, 0], [3, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 3, 0, 0], [3, 2, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [3, 2, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 2]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 0, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 2]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 1, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 2]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]],[[3, 3, 0, 0], [3, 3, 1, 1], [2, 2, 3, 2], [3, 3, 3, 3]],[[3, 2, 1, 0], [3, 3, 1, 1], [3, 2, 3, 2], [3, 3, 3, 3]],[[3, 3, 3, 0], [3, 3, 3, 1], [3, 3, 3, 2], [3, 3, 3, 3]]]
twelve_elem_magma = [[[5, 11, 3, 5, 0, 0, 11, 6, 0, 0, 11, 6],
 [4, 2, 1, 4, 1, 1, 4, 1, 1, 1, 4, 1],
 [2, 2, 7, 2, 8, 4, 4, 2, 4, 8, 2, 8],
 [5, 11, 3, 5, 3, 3, 11, 1, 3, 3, 11, 1],
 [4, 4, 7, 4, 7, 4, 4, 4, 4, 8, 4, 8],
 [5, 5, 7, 5, 5, 4, 4, 5, 10, 5, 5, 5],
 [5, 5, 10, 5, 6, 10, 4, 6, 10, 6, 5, 6],
 [9, 7, 7, 9, 7, 7, 7, 1, 7, 7, 7, 8],
 [8, 8, 7, 8, 8, 4, 4, 8, 10, 8, 8, 8],
 [9, 9, 7, 9, 7, 9, 9, 9, 9, 8, 9, 8],
 [9, 4, 10, 4, 10, 10, 9, 10, 10, 10, 4, 10],
 [9, 11, 7, 9, 7, 11, 11, 9, 11, 7, 11, 8]]]
three_elem_magmas = [magma for magma in [[[t[3*i+j] for i in range(3)] for j in range(3)] for t in itertools.product(range(3), repeat=9)] if check_854(magma)]
all_magmas = three_elem_magmas + four_elem_magmas + twelve_elem_magma