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 <bits/stdc++.h>
using namespace std;
#define rep(i,cc,n) for(int i=cc;i<n;++i)
#define lrep(i,cc,n) for(long long i=cc;i<n;++i)
#define sqrep(i,cc,n) for(long long i=cc;i*i<=n;++i)
#define rrep(i,cc,n) for(long i=cc;i>n;--i)
#define pii pair<int, int>
#define pll pair<long long, long long>
 
using ll = long long;
const ll inf = 1001001001;
const ll mod = 1000000007;
 
int main() {
    int n;
    cin >> n;
    int cnt1=0,cnt2=0,cnt3=0, ans=0;  
    rep(i, 0, n){
        string a;
        cin >> a;
        int m = a.size();
        rep(j, 0, m-1){
            if(a[j]=='A'&&a[j+1]=='B')ans++;
        }
        if(a[0]!='B'&& a[m-1]=='A')cnt1++;
        if(a[0]=='B'&& a[m-1]!='A')cnt2++;
        if(a[0]=='B'&& a[m-1]=='A')cnt3++;
    }
    //cout << ans << endl;
    if(cnt1>cnt2){
        if(cnt3!=0)ans += cnt2+cnt3;
        else ans += cnt2;
    }
    if(cnt1<cnt2){
        if(cnt3!=0)ans += cnt1+cnt3;
        else ans += cnt1;
    }
    if(cnt1 == cnt2){
        if(cnt1==0)ans += cnt3 -1; 
        else ans += cnt1+cnt3;
    }
    cout << ans << endl;
    //cout << cnt1 << cnt2 << cnt3 << endl;
}