Maximal Square Area

Complete the function below. The function receives the full standard input as a single string and must return the exact standard output lines for the described problem.

Problem

Given an m x n matrix of characters '0' and '1', find the largest square containing only '1's and return its area.

Input

First line: two integers m n

Next m lines: each is a length-n string containing only 0/1

Output

A single integer: the maximal square area

Constraints

1 <= m, n <= 300

Examples

4 5

10100

10111

11111

10010

Output:

4

2 2

00

Output:

0

Example

Input

4 5

10100

10111

11111

10010

Output

4

Complete solveMaximalSquareArea. It has one parameter, String input, containing the full stdin payload. Return the stdout payload as an array of lines, without trailing newline characters.