import numpy as np

def solution(g):
    #print_grid(g)
    grid = np.array(g)
    #print grid
    height, width = grid.shape
    #print height, width

    memo = {}
    prev_cases = {i:1 for i in range(2**(height+1))}
    #for i in range(2**(height+1)):
    #    prev_cases[i] = 1
    #    memo[i] = {j:calculate_c_column(i, j, height) for j in range(2**(height+1))}
    #print memo

    #print prev_cases
    for column in range(width):
        cases = {}
        c = list_to_int(grid[:,column])
        #print grid[:,column], 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]
        #print cases
        prev_cases = cases
    return sum(prev_cases.values())

def print_grid(g):
    for row in g:
        line = ""
        for elem in row:
            if elem:
                line+="O"
            else:
                line+="."
        print line

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
    #print ' '.join(('{:0'+str(length)+'b}').format(k) for k in [i, j]), ' '.join(('{:0'+str(length-1)+'b}').format(k) for k in [multiple_ones, odd_ones, single_one])
    return single_one

#l=3
#memo = {}
#for i in range(2**(l-1)):
#    memo[i] = 0
#for i in range(2**l):
#    for j in range(2**l):
#        t = calculate_c_column(i, j, l)
#        memo[t] += 1
#print memo
#exit(0)

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),
            #([[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)