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<algorithm>
#include<string>
using namespace std;
int main(){
	int N;
  cin>>N;
  string s;
  int count_ab=0;
  int count_b=0;
  int count_a=0;
  
  int count_ba=0;
  int b=0,a=0;
  
  for(int i=0;i<N;i++){
    s="";
  	cin>>s;
    a=0;
    b=0;
    for(int j=0;j<s.size();j++){
      a=0;
      b=0;
    	if(j==0){
        	if(s[0]=='B'){
              b=1;
            }
        }else if(s[j]=='B'){
        	if(s[j-1]=='A'){
            	count_ab++;
            }
        }else if(j==(s.size()-1)){
        	if(s[j]=='A'){
              a=1;
            }
        }
      
      
      if(a && b){
      	count_ba++;
      }else if(a){
      	count_a++;
      }else if(b){
      	count_b++;
      }
      
    
    }
    
  }
  int ans=0;
  
  if(count_ba>0){
  	if((count_a!=0)&&(count_b!=0)){
    	ans=count_ba+1;
      count_a--;
      count_b--;      
    }else if(count_a!=0){
    	ans=count_ba;
      count_a--;
    }else if(count_b!=0){
    	ans=count_ba;
      count_b--;
    }
  }
  ans+=count_ab+min(count_a,count_b);
	cout<<ans;
  return 0;
}