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>
int main(){
  int N,i,k;
  int A = 0;
  int B = 0;
  int C = 0;
  char S[11111][10];
  scanf("%d",&N);
  for(i=0;i<=N-1;i++)
    scanf("%s",S[i]);
  int count = 0;
  for(i=0;i<=N-1;i++)
    for(k=0;k<=8;k++)
      if(S[i][k] == 'A' && S[i][k+1] == 'B') count++;
  int length[11111] = {0};
  for(i=0;i<=N-1;i++)
    while(S[i][length[i]]) length[i]++;
  for(i=0;i<=N-1;i++)
    if(S[i][0] == 'B' && S[i][length[i]-1] != 'A') B++;
  for(i=0;i<=N-1;i++)
    if(S[i][length[i]-1] == 'A' && S[i][0] != 'B') A++;
  for(i=0;i<=N-1;i++)
    if(S[i][length[i]-1] == 'A' && S[i][0] == 'B') C++;
  int D ;
  if(A>0 && B>0 && A > B) D = C + B;
  if(A>0 && B>0 && A <= B) D = C + A;
  if(A==0 && B>0) D = C;
  if(A==0 && B==0 && C>0) D = C - 1;
  if(A==0 && B==0 && C==0) D = 0;
  if(A>0 && B==0) D = C;
  count += D;
  printf("%d",count);
}