Mock CCC '18 Contest 5 S5 - California Boggle

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Points: 20 (partial)
Time limit: 1.0s
Java 2.0s
Memory limit: 1G

Problem type

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.


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


Sample Output



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