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(a,b) ((a < b) ? a : b)

int main(void) {
  int N = 0;
  scanf("%d", &N);
  int headB = 0;
  int tailA = 0;
  int bothBA = 0;
  int midAB = 0;
  for(int i = 0; i < N; i++) {
    char s[11];
    scanf("%s", s);
    int len = strlen(s);
    if(s[0] == 'B' && s[len-1] == 'A') {
      bothBA++;
    }
    if(s[0] == 'B') {
      headB++;
    }
    if(s[len-1] == 'A') {
      tailA++;
    }
    for(int i = 1; i < len; i++) {
      if(s[i-1] == 'A' && s[i] == 'B') {
	midAB++;
      }
    }
  }

  int onlyA = tailA - bothBA;
  int onlyB = headB - bothBA;
  int K = MIN(onlyA, onlyB);
  int X = midAB + K;

  if(onlyA == onlyB) {
    if(bothBA > 0)
      X += (bothBA - 1);
  } else if(onlyA < onlyB) {
    // no only A
    K = MIN(onlyB, bothBA);
    X += K;
    if(onlyB < bothBA) {
      if(bothBA > 0)
	X += (bothBA - 1);
    }
  } else {
    // no only B
    K = MIN(onlyA, bothBA);
    X += K;
    if(onlyA < bothBA) {
      if(bothBA > 0)
	X += (bothBA - 1);
    }
  }
  
  printf("%d\n", X);
  return 0;
}