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 5.4.1) (judge verdict: Wrong Answer)

#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdio.h>
int compare(const void *a,const void *b){
    if(*(long long*)a>*(long long *)b)return 1;
    return -1;
}
int MIN(int a,int b){
    return a<b?a:b;
}
int main()
{   int n;
    scanf("%d",&n);
    char s[n][11];
    for(int i=0;i<n;i++){
        scanf("%s",s[i]);
    }
    int inner=0;
    for(int i=0;i<n;i++){
        int l=strlen(s[i]);
        for(int j=0;j<l-1;j++){
            if(s[i][j]=='A'&&s[i][j+1]=='B'){
                inner++;
                //printf("inner incre@i%d,j%d",i,j);
            }
        }
    }
    int ht=0,h=0,t=0;
    for(int i=0;i<n;i++){
        int l=strlen(s[i]);
        if(s[i][0]=='B'&&s[i][l-1]=='A'){
            ht++;
        }else if(s[i][0]=='B'){
            h++;
        }else if(s[i][l-1]=='A'){
            t++;
        }
    }
    if(h>0){ht++;
    h--;}
    if(t>0){ht++;
    t--;
    }
    //printf("inner%d ht%d h%d t%d\n",inner,ht,h,t);
    printf("%d",ht-1+MIN(h,t)+inner);
    
    return 0;
}