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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

int main(){
  int n;
  int c1,c2,c3;
  int counter=0;
  c1=0;c2=0;c3=0;
  string s;
  cin>>n;
  rep(i,n){
    cin>>s;

    rep(j,s.length()-1){
      if(s.at(j)=='A'&&s.at(j+1)=='B') counter++;
    }
    
    if(s.at(0)=='B'&&s.at(s.length()-1)=='A') c1++;
    else if(s.at(0)=='B') c2++;
    else if(s.at(s.length()-1)=='A') c3++;
  }

  if(c2==0&&c3==0){
    if(c1==0)cout<<counter<<endl;
    else{
      cout<<counter+c1-1<<endl;
    }
    return 0;
  }

  int x;
  x=min(min(c1,c2),c3);
  c1-=x;c2-=x;c3-=x;
  x*=2;
  int y;
  if(c1==0){
    y=min(c2,c3);
    
  }
  else if(c2==0){
    y=min(c3,c1);
    if(c1-y>0){
      y+=(c1-y);
    }
  }
  else if(c3==0){
    y=min(c2,c1);
    if(c1-y>0){
      y+=(c1-y);
    }
  }
  cout<<counter+x+y<<endl;
  
}