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<string>
#include<vector>
#include<algorithm>

using namespace std;

int gcd(int a, int b){
    if(a == 0)return b;
    if(b == 0)return a;
    if(a < b){
        int tmp = a;
        a = b;
        b = tmp;
    }
    int r = a % b;
    if(r == 0)return b;
    return gcd(b, r);
}

int main(){
    int N;
    cin >> N;

    string s[N];
    for(int i = 0; i < N; i++)cin >> s[i];

    int countA = 0;
    int countB = 0;
    int pair = 0;

    int count = 0;
    for(int i = 0; i < N; i++){
        for(int j = 0; j < s[i].size(); j++){
            if(s[i][j] == 'A' && s[i][j+1] == 'B'){
                count++;
            }
        }
        if(s[i][s[i].size() - 1] == 'A')countA++;
        if(s[i][0] == 'B')countB++;
        if(s[i][0] == 'B' && s[i][s[i].size() - 1] == 'A'){
            pair++;
            countB--;
            countA--;
        }
    }
    if(pair > 0){
        count += pair - 1;
        countA++;
        countB++;
    }
    if(countA < countB)count += countA;
    else count += countB;

    if(pair > 0 && countA == 1 && countB == 1)count--;
    cout << count;

    return 0;
}