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 <stdio.h>
#include <string.h>
#define min(x, y) ((x<y) ? (x) : (y))

int main(){
    int N, i, j, ans = 0;
    scanf("%d", &N);

    int SN[N];
    char S[N][10];
    for (i=0; i<N; i++){
        scanf("%s", &S[i]);
        SN[i] = strlen(S[i]);
    }

    int A=0, B=0, AB=0;
    for (i=0; i<N; i++){
        if (S[i][0] == 'B' && S[i][SN[i]-1] == 'A'){
            AB++;
            continue;
        }
        if (S[i][0] == 'B'){
            B++;
            continue;
        }
        if (S[i][SN[i]-1] == 'A'){
            A++;
            continue;
        }
    }

    for (i=0; i<N; i++){
        for (j=0; j<SN[i]-1; j++){
            if (S[i][j] == 'A' && S[i][j+1] == 'B'){
                ans++;
            }
        }
    }

    if (AB>0) ans += AB-1;
    if (A>0 || B>0){
        ans++;
        if (A>B){
            A--;
        }else{
            B--;
        }
    }

    ans += min(A, B);
 
    printf("%d", ans);
    return 0;
}