Given an $N\times N$ grid of letters, one can select four squares such that the first is a C, the second is an A, the third is an L, and the last is an I, and two adjacent squares in the pattern share at least a corner.

This selection process is repeated as many times as possible, with the caveat that a given square can only be selected at most once.

Compute the maximum number of distinct sets of letters that can be selected.

Constraints

$1\le N\le 200$

In tests worth $3$ marks, you may assume $N\le 4$.

In tests worth an additional $5$ marks, you may assume $N\le 10$.

Input Specification

The first line of the input contains a single integer, $N$.

The next $N$ lines contain $N$ characters, all of which appear in CALI.

Output Specification

Output, on a single line, the maximum number of sets that can be selected.

Sample Input

4
CALI
ILAC
CLLC
IAAI

Sample Output

4