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: Accepted)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <queue>

using namespace std;

int main() {
    int n;
    cin >> n;
    
    vector<string> v(n);
    for(int i = 0; i < n; i++) {
        cin >> v[i];
    }
    
    int cnt[3] = {0};
    int ans = 0;
    for(int i = 0; i < n; i++) {
        if(v[i][0] == 'B' && v[i][v[i].size() - 1] == 'A') {
            cnt[0]++;
        }
        else if(v[i][0] == 'B') {
            cnt[1]++;
        }
        else if(v[i][v[i].size() - 1] == 'A') {
            cnt[2]++;
        }
        
        for(int j = 0; j < v[i].size(); j++) {
            if(v[i][j] == 'A') {
                if(j < n - 1 && v[i][j + 1] == 'B') {
                    ans++;
                }
            }
        }
    }
    
    if(cnt[0] > 0) {
        ans += cnt[0] - 1;
        if(cnt[1] > 0) {
            ans++;
            cnt[1]--;
        }
        if(cnt[2] > 0) {
            ans++;
            cnt[2]--;
        }
    }
    
    ans += min(cnt[1], cnt[2]);
    
    cout << ans << endl;
    
    return 0;
}