# Time:  ctor:   O(m * n),
#        lookup: O(1)
# Space: O(m * n)

class NumMatrix(object):
    def __init__(self, matrix):
        """
        initialize your data structure here.
        :type matrix: List[List[int]]
        """
        if not matrix:
            return

        m, n = len(matrix), len(matrix[0])
        self.__sums = [[0 for _ in xrange(n+1)] for _ in xrange(m+1)]
        for i in xrange(1, m+1):
            for j in xrange(1, n+1):
                self.__sums[i][j] = self.__sums[i][j-1] + matrix[i-1][j-1]
        for j in xrange(1, n+1):
            for i in xrange(1, m+1):
                self.__sums[i][j] += self.__sums[i-1][j]

    def sumRegion(self, row1, col1, row2, col2):
        """
        sum of elements matrix[(row1,col1)..(row2,col2)], inclusive.
        :type row1: int
        :type col1: int
        :type row2: int
        :type col2: int
        :rtype: int
        """
        return self.__sums[row2+1][col2+1] - self.__sums[row2+1][col1] - \
               self.__sums[row1][col2+1] + self.__sums[row1][col1]