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# Runtime: 3180 ms (Top 18.96%) | Memory: 24.7 MB (Top 69.46%)
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class NumMatrix:
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    def __init__(self, matrix: List[List[int]]):
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        m, n = len(matrix), len(matrix[0])
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        # Understand why we need to create a new matrix with extra one row/column
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        self.sum = [[0 for row in range(n + 1)] for column in range(m + 1)]
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        for r in range(1, m + 1):
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            for c in range(1, n + 1):
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                self.sum[r][c] = (
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                    self.sum[r - 1][c]
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                    + self.sum[r][c - 1]
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                    - self.sum[r - 1][c - 1]
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                    + matrix[r - 1][c - 1]
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                )
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    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
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        r1, c1, r2, c2 = row1 + 1, col1 + 1, row2 + 1, col2 + 1
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        return (
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            self.sum[r2][c2]
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            - self.sum[r1 - 1][c2]
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            - self.sum[r2][c1 - 1]
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            + self.sum[r1 - 1][c1 - 1]
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        )
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# Your NumMatrix object will be instantiated and called as such:
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# obj = NumMatrix(matrix)
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# param_1 = obj.sumRegion(row1,col1,row2,col2)