Number of constant square submatrices

Each case of the input in this exercise is a matrix of 0s and 1s. The program has to compute the total number of non-empty submatrices that are square and constant (same number of rows and columns and the same symbol). For instance, consider this as the input matrix:

It has 1 constant submatrix of size $3\times{}3$ (with 0s), 6 constant submatrices $2\times{}2$ (4 of them with 0s, and 2 of them with 1s), and 20 constant submatrices $1\times{}1$ . Therefore, in this case the output would be $27$ .

Input

The input has several cases. Each case starts with a line with two positive naturals $n$ and $m$ . After that come $n$ lines with $m$ characters, either $0$ or $1$ , which describe a matrix of size $n\times{}m$ , followed by an empty line.

Output

For each case, the program must write the total number of non-empty square submatrices in one line.

Observation

Evaluation out of 10 points:

Slow solution: 5 points.
Fast solution: 10 points.

A fast solution is one which is correct, of linear cost and passing the test cases, both public and private. A slow solution is one which is not fast, but it is correct and passes the public test cases.

Problem information

Author: PRO1

Generation: 2026-01-25T14:26:08.642Z