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Sort Matrix by Diagonals

You are given an n x n square matrix of integers grid.

You are given an n x n square matrix of integers grid. Return the matrix such that:

Sort Matrix by Diagonals diagram

Example 1

Input: grid = [[1,7,3],[9,8,2],[4,5,6]]

Output: [[8,2,3],[9,6,7],[4,5,1]]

Explanation: The diagonals with a black arrow (bottom-left triangle) should be sorted in non-increasing order: The diagonals with a blue arrow (top-right triangle) should be sorted in non-decreasing order:

Example 2

Input: grid = [[0,1],[1,2]]

Output: [[2,1],[1,0]]

Explanation: The diagonals with a black arrow must be non-increasing, so [0, 2] is changed to [2, 0] . The other diagonals are already in the correct order.

Example 3

Input: grid = [[1]]

Output: [[1]]

Explanation: Diagonals with exactly one element are already in order, so no changes are needed.

Constraints

  • grid.length == grid[i].length == n
  • 1 <= n <= 10
  • -10^5 <= grid[i][j] <= 10^5

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