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Maximum Size Square Sub-matrix


Problem Description

Given a 2D binary matrix A of size N x M find the area of maximum size square sub-matrix with all 1's.



Problem Constraints

1 <= N, M <= 103

A[i][j] = 1 or A[i][j] = 0



Input Format

First argument is an 2D matrix A of size N x M.



Output Format

Output the area of maximum size square sub-matrix in A with all 1's.



Example Input

Input 1:

 A = [
[0, 1, 1, 0, 1],
[1, 1, 0, 1, 0],
[0, 1, 1, 1, 0],
[1, 1, 1, 1, 0],
[1, 1, 1, 1, 1],
[0, 0, 0, 0, 0] ]

Input 2:

 A = [
[1, 1], [1, 1] ]



Example Output

Output 1:

 9

Output 2:

 4



Example Explanation

Explanation 1:

  Consider the below binary matrix.
 
 The area of the square is 3 * 3 = 9

Explanation 2:

 The given matrix is the largest size square possible so area will be 2 * 2 = 4



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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