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 <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <stack>
#include <queue>
#define llong long long
#define INF (__INT32_MAX__ / 2)
#define MAX_N 10000

using namespace std;
typedef pair<int, int> ipair;

int N;
string str[MAX_N];

int solve() {
    int res = 0;

    for(int i = 0; i < N; ++i) {
        for(int j = 0; j < str[i].size() - 1; ++j)
            if(str[i][j] == 'A' && str[i][j + 1] == 'B')
                ++res;
    }

    int _a = 0;
    int b_ = 0;
    int b_a = 0;
    for(int i = 0; i < N; ++i) {
        if(str[i][0] == 'B' && str[i][str[i].size() - 1] == 'A')
            ++b_a;
        else if(str[i][0] == 'B')
            ++b_;
        else if(str[i][str[i].size() - 1] == 'A')
            ++_a;
    }

    res += min(_a, b_);

    if(b_ < _a) {
        res += b_a;
    } else if (b_ > _a) {
        res += b_a;
    } else {
        if(_a == 0)
            res += b_a - 1;
        else {
            res += b_a;
        }
    }

    return res;
}

int main(int argc, char **argv) {
    cin >> N;
    for(int i = 0; i < N; ++i)
        cin >> str[i];

    cout << solve() << endl;
}