class PixPix:
    def __init__(self, a, b, c, d):
        self.a, self.b, self.c, self.d = a, b, c, d

    def __mul__(self, x):
        a, b, c, d = self.a, self.b, self.c, self.d
        e, f, g, h = x.a, x.b, x.c, x.d
        if d == e and c == f:
            return PixPix(a, b, g, h)

    def __repr__(self):
        return '[{},{},{},{}]'.format(self.a, self.b, self.c, self.d)

    def __eq__(self, x):
        return (self.a, self.b, self.c, self.d) == (x.a, x.b, x.c, x.d)

class Maxel:
    def __init__(self, *pixs):
        self.pixs = pixs

    def __add__(self, x):
        return Maxel(self.pixs + x.pixs)

    def __mul__(self, x):
        return Maxel(*(i*j for i in self.pixs for j in x.pixs if i*j is not None))

    def __repr__(self):
        return '[' + ' '.join(map(repr, self.pixs)) + ']'

    def __eq__(self, x):
        if len(self.pixs) != len(x.pixs):
            return False
        a = list(self.pixs)
        b = list(x.pixs)
        while a:
            if a[0] not in b:
                return False
            b.remove(a[0])
            a.remove(a[0])
        return True

    def __pow__(self, n):
        assert n == int(n) and n >= 1
        a = self
        for _ in range(n-1):
            a *= self
        return a

m = Maxel(PixPix(2,1,1,1), PixPix(2,2,2,1), PixPix(1,1,2,2), PixPix(1,2,1,2))

"""

>>> m
[[2,1,1,1] [2,2,2,1] [1,1,2,2] [1,2,1,2]]
>>> m**4
[[2,1,1,2] [2,2,2,2] [1,1,1,1] [1,2,2,1]]
>>> m**4 == (m**4)*(m**4)
True
>>> m == m**5
True
>>> m**2 == m**4
False
>>> [[2*p.a+p.b-2, 2*p.d+p.c-2] for p in m.pixs]
[[3, 1], [4, 2], [1, 4], [2, 3]]

Record [3,1] etc in a matrix.

[0 0 0 1; 0 0 1 0; 1 0 0 0; 0 1 0 0] = [0 -1; 1 0] = i

"""