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<iostream>
#include<cstdlib>
#include<string>
#include<vector>
using namespace std;

int main(void){
  int n; cin>>n;
  vector<string> v(n);
  for(int i=0; i<n; ++i) cin>>v[i];

  long count=0;
  int count_begin_b=0, count_end_a=0, count_ba_in=0;

  for(int i=0; i<n; ++i){
    bool is_prev_a = false;
    bool is_begin_b = false;
    for(int j=0; j<v[i].size(); ++j){
      if( j == 0 && v[i][j] == 'B'){
        count_begin_b++;
        is_begin_b = true;
      }
      else if( j == v[i].size()-1 && v[i][j] == 'A'){
        count_end_a++;
        if( is_begin_b ) count_ba_in++;
      }

      if( is_prev_a && v[i][j] == 'B') count++;
      if( v[i][j] == 'A') is_prev_a = true;
      else is_prev_a = false;
    }
  }

  count += count_ba_in-1;
  count_begin_b -= count_ba_in;
  count_end_a -= count_ba_in;
  if( count_begin_b == count_end_a) count += count_begin_b + 1;
  else count += min(count_begin_b, count_end_a)+1;
  
  cout<< count <<endl;

  return 0;
}