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Equal Sum Grid Partition I

You are given an m x n matrix grid of positive integers.

You are given an m x n matrix grid of positive integers. Your task is to determine if it is possible to make either one horizontal or one vertical cut on the grid such that:

Return true if such a partition exists; otherwise return false.

Equal Sum Grid Partition I diagram

Example 1

Input: grid = [[1,4],[2,3]]

Output: true

Explanation: A horizontal cut between row 0 and row 1 results in two non-empty sections, each with a sum of 5. Thus, the answer is true .

Example 2

Input: grid = [[1,3],[2,4]]

Output: false

Explanation: No horizontal or vertical cut results in two non-empty sections with equal sums. Thus, the answer is false .

Constraints

  • 1 <= m == grid.length <= 10^5
  • 1 <= n == grid[i].length <= 10^5
  • 2 <= m * n <= 10^5
  • 1 <= grid[i][j] <= 10^5

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