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