# Time:  O(m * n)
# Space: O(m * n)

import collections


class Solution(object):
    def findBlackPixel(self, picture, N):
        """
        :type picture: List[List[str]]
        :type N: int
        :rtype: int
        """
        rows, cols = [0] * len(picture),  [0] * len(picture[0])
        lookup = collections.defaultdict(int)
        for i in xrange(len(picture)):
            for j in xrange(len(picture[0])):
                if picture[i][j] == 'B':
                    rows[i] += 1
                    cols[j] += 1
            lookup[tuple(picture[i])] += 1

        result = 0
        for i in xrange(len(picture)):
            if rows[i] == N and lookup[tuple(picture[i])] == N:
                for j in xrange(len(picture[0])):
                     result += picture[i][j] == 'B' and cols[j] == N
        return result


class Solution2(object):
    def findBlackPixel(self, picture, N):
        """
        :type picture: List[List[str]]
        :type N: int
        :rtype: int
        """
        lookup = collections.Counter(map(tuple, picture))
        cols = [col.count('B') for col in zip(*picture)]
        return sum(N * zip(row, cols).count(('B', N)) \
                   for row, cnt in lookup.iteritems() \
                   if cnt == N == row.count('B'))