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 <iostream>
#include <algorithm>
#include <string>

using namespace std;



int main(){

    int n;
    string s;

    cin >> n;

    int b = 0;
    int a = 0;
    int ba = 0;
    int ab = 0;

    for(int i = 0; i < n; i++){
        cin >> s;

        for(int j = 0; j < s.size() - 1; j++){
            if(s[j] == 'A' && s[j + 1] == 'B') ab++;
        }

        if(s[0] == 'B' && s[s.size() - 1] == 'A'){
            ba++;
        }else if(s[0] == 'B'){
            b++;
        }else if(s[s.size() - 1] == 'A'){
            a++;
        }

    }

    cerr << ab << " " <<  ba << " " <<  b << " " << a << endl;

    int k = 0;

    if(ba > 0){
        k = ba - 1;

        if(k > 0 && b > 0){
            k++;
            b--;
        }
        if(k > 0 && a > 0){
            k++;
            a--;
        }

        k = k + min(a,b);

    }else{
        k = min(a,b);
    }

    cout << ab + k << endl;

    return 0;
}