Problem:
Score : 400 points

Problem Statement

Snuke has N strings. The i-th string is s_i.

Let us concatenate these strings into one string after arranging them in some order.
Find the maximum possible number of occurrences of AB in the resulting string.

Constraints

1 \leq N \leq 10^{4}

2 \leq |s_i| \leq 10

s_i consists of uppercase English letters.

Input

Input is given from Standard Input in the following format:

N
s_1
\vdots
s_N

Output

Print the answer.

Sample Input 1

3
ABCA
XBAZ
BAD

Sample Output 1

2

For example, if we concatenate ABCA, BAD and XBAZ in this order, the resulting string ABCABADXBAZ has two occurrences of AB.

Sample Input 2

9
BEWPVCRWH
ZZNQYIJX
BAVREA
PA
HJMYITEOX
BCJHMRMNK
BP
QVFABZ
PRGKSPUNA

Sample Output 2

4

Sample Input 3

7
RABYBBE
JOZ
BMHQUVA
BPA
ISU
MCMABAOBHZ
SZMEHMA

Sample Output 3

4

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include"bits/stdc++.h"

using namespace std;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int N;
	cin >> N;
	int ans = 0;
	int cnt_BA = 0;
	int cnt_A = 0;
	int cnt_B = 0;
	string A;

	for (int i = 0; i < N; i++)
	{
		cin >> A;
		for (int j = 1; j < A.size(); j++) {
			if (A[j - 1] == 'A'&&A[j] == 'B') {
				ans++;
			}
		}
		if (A[0] == 'B' && A[A.size() - 1] == 'A') {
			cnt_BA++;
		}
		else if (A[0] == 'B') {
			cnt_B++;
		}
		else if (A[A.size()-1] == 'A') {
			cnt_A++;
		}
	}
	if (cnt_A + cnt_B == 0 && ans > 0) {
		ans += cnt_BA - 1;
	}
	else {
		ans += cnt_BA + min(cnt_A, cnt_B);
	}
	cout << ans << endl;

	return 0;
}