Maximal Square

Given a binary matrix, find out the largest size square sub-matrix with all 1's and return its area.

Input & Output

Input

matrix — a binary matrix

Output

the area of the largest square in the input matrix

Example

Input

matrix = 
[[1, 0, 1, 0, 0],
 [1, 0, 1, 1, 1],
 [1, 1, 1, 1, 0],
 [1, 0, 0, 1, 0]]

Output

Explanation

The largest square is of size 2x2 and area 4.

Constraints

Try it yourself