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

 

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: