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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, a, b) for(int i = a; i < b; i++)
#define  all(x) (x).begin(),(x).end()     // 昇順ソート
#define  rall(v) (v).rbegin(), (v).rend() // 降順ソート
#define  FastIO ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0)
typedef long long ll;
using P = pair<int,int>;
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return true; } return false; }

int main(){
    int n;
    cin >> n;
    vector<string> s(n);
    rep(i,n) cin >> s[i];
    int ab = 0, a = 0, b = 0, ans = 0;
    rep(i,n){
        string si = s[i];
        int sz = si.size();
        rep(j, sz-1){
            if (si.substr(j, 2) == "AB") ans++;
        }
        if (si[0] == 'B' && si[sz-1] == 'A') ab++;
        else if (si[0] == 'B') b++;
        else if (si[sz-1] == 'A') a++;
    }
    int minNum = min(a, b);
    if (ab > 0){
        ab += minNum;
        a -= minNum;
        b -= minNum;
        ans += ab - 1;
        if (a != 0 || b != 0) ans++;
    }else {
        ans += minNum;
    }
    cout << ans << endl;
    return 0;
}