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<string>
using namespace std;

int main(){
        int n=0;
        cin >> n;
        string tmp;
        int ba_num = 0;
        int last_a=0;
        int first_b=0;
        int ans = 0;
        for(int i=0;i<n;i++){
                cin >> tmp;
                int len=(int)(tmp.length());
                for(int i=0;i<len-1;i++){
                        if(tmp[i]=='A' & tmp[i+1] == 'B'){
                                ans++;
                                i++;
                        }
                }
                bool first_is_b, last_is_a;
                if(first_is_b = (tmp[0] == 'B')) first_b++;
                if(last_is_a = (tmp[len-1] == 'A')) last_a++;
                if(first_is_b | last_is_a) ba_num++;
        }
        ans += min(last_a, first_b);
        if(last_a==first_b) ans--;
        cout << ans << endl;
        return 0;
}