Count Square Submatrices

Statement

Given an N ∗ M matrix containing only ones and zeros, count the total number of square submatrices that contain only 1’s.

Example

Consider the input matrix given below. We have a total of $7$ square submatrices with all ones, including $6$ square matrices of order 1 x 1 and $1$ square matrix of order 2 x 2.

Sample input

[
  [1,0,1],
  [1,1,0],
 

...