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class Solution(object):
    def maximalRectangle(self, mat):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """
        if len(mat) == 0 or len(mat[0]) == 0:
            return 0
        H = len(mat)
        W = len(mat[0])
        largest = 0
        heights = [0]*(W+1)
        for j in range(H):
            for i in range(W):
                if mat[j][i] == '1':
                    heights[i] += 1
                else:
                    heights[i] = 0
            stack = []
            for i in range(W+1):
                while len(stack) != 0 and heights[stack[-1]] > heights[i]:
                    temp = stack[-1]
                    del stack[-1]
                    leftWidth = temp if len(stack) == 0 else temp-stack[-1]-1
                    rightWidth = i-temp-1
                    largest = max(largest, (leftWidth + rightWidth + 1) * heights[temp])
                stack.append(i)
        return largest