import numpy as np

def solution(g):
    grid = np.array(g)
    height, width = grid.shape
    
    prev_cases = {i:1 for i in generate_prev_cases(grid[:, 0])}
    memo = {}

    for column in range(width):
        cases = {}
        c = list_to_int(grid[:, column])
        for i in prev_cases.keys():
            if not i in memo:
                memo[i] = {}
            if not c in memo[i]:
                memo[i][c] = [j for j in range(2**(height+1)) if calculate_c_column(i, j, height) == c]
            for j in memo[i][c]:
                if not j in cases:
                    cases[j] = 0
                if i in prev_cases:
                    cases[j] += prev_cases[i]
        prev_cases = cases
    return sum(prev_cases.values())

def generate_prev_cases(column):
    if len(column) == 0:
        yield 0
        yield 1
    else:
        for v in generate_prev_cases(column[:-1]):
            if column[len(column)-1] and v&1 == 1:
                yield v<<1|0
            else:
                yield v<<1|0
                yield v<<1|1

def calculate_c_column(i, j, length):
    mask = 2**length-1
    multiple_ones = ((i&j) | ((i&j)>>1)) & mask
    odd_ones = ((i^j) ^ ((i^j)>>1)) & mask
    single_one = (~multiple_ones & odd_ones) & mask
    return single_one

def list_to_int(l):
    value = 0
    for v in l:
        value |= v
        value <<= 1
    return value >> 1

tests = [
            ([[True, True, False, True, False, True, False, True, True, False], [True, True, False, False, False, False, True, True, True, False], [True, True, False, False, False, False, False, False, False, True], [False, True, False, False, False, False, True, True, False, False]], 11567),
            ([[True, False, True], [False, True, False], [True, False, True]], 4),
            ([[True, False, True, False, False, True, True, True], [True, False, True, False, False, False, True, False], [True, True, True, False, False, False, True, False], [True, False, True, False, False, False, True, False], [True, False, True, False, False, True, True, True]] ,254),
            ([[True]], 4),
            ([[False]], 12),
            ([[True, True]], 6),
            ([[True, False]], 10),
            ([[False, True]], 10),
            ([[False, False]], 38),
            # to test time consumption, the answer is not correct
            ([[True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False]], 1),
        ]

for (i, o) in tests:
    result = solution(i)
    print(i, result == o, result, o)