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;
using namespace std::chrono;
#define idfc ios_base::sync_with_stdio(false),cin.tie(nullptr),cout.tie(nullptr)
//:/
#define pb push_back
#define mp make_pair
#define nt _ll128
#define ld long double
long double PI =3.14159265358979323846;
using ll = long long;



const ll modo=998244353;
const ll inf=1e17;
const ll ms=(1e5)+5;

ll ar[ms]={0};
ll dp[ms][2]={0};

int go(int a,int b,int c)
{

    int r=0;
    if(a)
    {
        r+=c;
        if(b){r++; b--;}
        r+=min(a-1,b);
    }
    else if(c)
    {
        r=c-1;
        if(b)r++;
    }
  cout<<r<<endl;
    return r;
}

int main()
{
    idfc;
    int n;
    cin>>n;
    int a=0;
    int b=0;
    int c=0;
    int ans=0;
    string s;
    int len;int i;
    while(n--)
    {
        cin>>s;
        len=s.length();
        for(i=1;i<len;i++)
        {
            if(s[i-1]=='A'&&s[i]=='B')ans++;
        }
        if(s[0]=='B'&&s[len-1]=='A')c++;
        else if(s[0]=='B')b++;
        else if(s[len-1]=='A')a++;
    }

    int aa=ans+go(a,b,c);
 //   cout<<a<<" "<<b<<" "<<c<<endl;    
    cout<<aa;
    return 0;
}