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 cnt[3];

int main() {
    int ans = 0;
    
    int n; cin >> n;
    for (int i = 1; i <= n; ++i) {
        string s; cin >> s;
        
        for (int j = 0; j + 1 < (int) s.length(); ++j) {
            if (s[j] == 'A' && s[j + 1] == 'B') {
                ++ans;
            }
        }
        
        if (s.front() == 'B' && s.back() == 'A') {
            ++cnt[2];
        } else if (s.front() == 'B') {
            ++cnt[0];
        } else {
            ++cnt[1];
        }
    }

    if (cnt[2] == 0) {
        ans += min(cnt[0], cnt[1]);
    } else {
        ans += cnt[2] - 1;
        cnt[2] = 1;
        if (cnt[0] > 0 || cnt[1] > 0) {
            ans += 1;
            ans += min(cnt[0], cnt[1]);
        }
    }
    
    cout << ans << endl;
    
    return 0;
}