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<bits/stdc++.h>
using namespace std;

int main(){
  int N;
  cin >> N;
  vector<string> s(N);
  for(int i = 0; i < N; i++){
      cin >> s[i];
  }
  int cnt = 0;
  for(int i = 0; i < N; i++){
      for(int j = 0; j < s[i].length() - 1; j++){
          if(s[i].substr(j,2) == "AB"){
              cnt++;
          }
      }
  }
  int A_cnt = 0;
  int B_cnt = 0;
  int cnt2 = 0;
  int cnt3 = 0;
  for(int i = 0; i < N; i++){
      if((s[i][s[i].length()-1] == 'A') && !(s[i][s[i].length()-1] == 'A'&&s[i][0] == 'B')) {
          A_cnt++;
      }
      if((s[i][0] == 'B')&& !(s[i][s[i].length()-1] == 'A'&&s[i][0] == 'B')){
          B_cnt++;
      }
      if(s[i][s[i].length()-1] == 'A' && s[i][0] == 'B'){
          cnt2++;
      }
  }
  cnt3 = min(A_cnt,B_cnt) + abs(cnt2-max(A_cnt,B_cnt)) /2;
  int ans = cnt + cnt3;
  cout << ans << endl;
}