Problem G
Palindromic Word Search

Given a rectangular grid of uppercase letters, find a rectangular region of the grid of maximum possible area such that there is a horizontal palindrome spanning some row of the rectangular region and a vertical palindrome spanning some column of the rectangular region. Recall a palindrome is a string that equals its own reversal.

Figure 1: Illustration of optimal solutions to the sample inputs. In the shaded subregions, a palindrome spanning an entire row of the region and a palindrome spanning an entire column of the region are highlighted.

Input

The first line contains two integers $R$ and $C$ ($1 \leq R,C \leq 500$). Then next $R$ lines describe the grid, each containing exactly $C$ uppercase letters.

Output

Output a single integer $A$ indicating the largest area of a rectangular region of the grid such that there is a horizontal palindrome spanning some row and a vertical palindrome spanning some column of the rectangular region.

4 5
APPLE
BOBBY
KAYAK
REBEL

15

2 6
ABCCDE
PRCDEE

4

4 6
BANANA
BERGEN
CANNOT
FELLOW

15