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;

#define REP(i,n) for(int i=0; i < (n); ++i)
#define REPR(i,n) for(int i=(n); i >=0; --i)
#define FOR(i, m, n) for(int i = (m); i < (n); ++i)

typedef long long ll;
#define INF 1e9

int main(){
  int N;
  cin >> N;
  ll ans = 0, cntAB = 0, cntA = 0, cntB = 0;
  vector<string> s(N);
  REP(i, N){
    cin >> s[i];
  }

  REP(i, N){
    for(int j = s[i].length()-1; j > 0; j--){
      if(s[i][j] == 'B' && s[i][j-1] == 'A'){
        ans++;
        j--;
      }
    }
  }

  REP(i, N){
    if(s[i][0] == 'B' && s[i][s[i].length()-1] == 'A'){
      cntAB++;
    }
    else if(s[i][0] == 'B'){
      cntB++;
    }
    else if(s[i][s[i].length()-1] == 'A'){
      cntA++;
    }
  }

  if(cntAB == 0){
    ans += min(cntA, cntB);
  }
  else if(cntA== cntB){
    ans += cntAB-1 + cntA;
  }
  else if(cntA == 0 || cntB==0){
    ans += cntAB;
  }
  else{
    ans += cntAB+min(cntA, cntB);
  }
  cout << ans << endl;

  return 0;
}