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Matrix Similarity After Cyclic Shifts

You are given an m x n integer matrix mat and an integer k.

You are given an m x n integer matrix mat and an integer k. The matrix rows are 0-indexed.

The following proccess happens k times:

Return true if the final modified matrix after k steps is identical to the original matrix, and false otherwise.

Matrix Similarity After Cyclic Shifts diagram

Example 1

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

Output: false

Explanation: In each step left shift is applied to rows 0 and 2 (even indices), and right shift to row 1 (odd index).

Example 2

Input: mat = [[1,2,1,2],[5,5,5,5],[6,3,6,3]], k = 2

Output: true

Example 3

Input: mat = [[2,2],[2,2]], k = 3

Output: true

Explanation: As all the values are equal in the matrix, even after performing cyclic shifts the matrix will remain the same.

Constraints

  • 1 <= mat.length <= 25
  • 1 <= mat[i].length <= 25
  • 1 <= mat[i][j] <= 25
  • 1 <= k <= 50

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