Palindromic Word Search

문제

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.

입력

The first line contains two integers $RR$ and $CC$ ($1\le R,C\le 5001\; \backslash leq\; R,C\; \backslash leq\; 500$). Then next $RR$ lines describe the grid, each containing exactly $CC$ uppercase letters.

출력

Output a single integer $AA$ 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.