# 2d S-G function for chomp

def mex(S):
    i = 0
    while i < len(S) and i in S:
        i += 1

    return i

def bite(state, x):
    ns = list(state)
    for i in range(x[1], len(ns)):
        ns[i] = x[0]

    return tuple(ns)

def empty(state):
    for e in state:
        if e != 0:
            return False

    return True

@CachedFunction
def SG(state):
    if empty(state):
        return mex([])

    s = []
    for i in range(len(state)):
        for j in range(state[i]):
            ns = bite(state, (j, i))
            s.append(SG(ns))

    return mex(s)


-------------------------------------
And second for 3d one:

# 3d S-G function for chomp

def mex3D(S):
    i = 0
    while i < len(S) and i in S:
        i += 1

    return i

def list_state(state):
    return [[j for j in l] for l in state]

def tuple_state(lstate):
    return tuple([tuple(l) for l in lstate])

def bite3D(state, x):
    ns = list_state(state)
    for i in range(x[1], len(ns)):
        for j in range(x[0], len(ns[i])):
            ns[i][j] = x[2]

    return tuple_state(ns)

def empty3D(state):
    for e in state:
        for f in e:
            if f != 0:
                return False

    return True

@CachedFunction
def SG3D(state):
    if empty3D(state):
        return mex([])

    s = []
    for i in range(len(state)):
        for j in range(len(state[i])):
            for k in range(state[i][j]):
                ns = bite3D(state, (j, i, k))
                s.append(SG3D(ns))

    return mex(s)

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