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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <algorithm>

using namespace std;

int main(){
  int N;
  int AB = 0;
  int B_A = 0;
  int X_A = 0;
  int B_X = 0;
  int result = 0;
  cin >> N;
  for (int i=0;i<N;i++) {
    bool b_flag = false;
    bool a_flag = false;
    string s;
    cin >> s;
    size_t l = s.size();
    if (s[0] == 'B') {
      b_flag = true;
    }
    if (s[l-1] == 'A') {
      a_flag = true;
    }
    if (a_flag && b_flag) {
      B_A++;
    } else if (a_flag) {
      X_A++;
    } else if (b_flag) {
      B_X++;
    }
    for (int i=0;i<l-1;i++) {
      if (s[i] == 'A' && s[i+1] == 'B') {
	AB++;
      }
    }
  }

  if (B_A > 0) {
    result += B_A - 1;
    if (X_A > 0) {
      result++;
      X_A--;
    }
    if (B_X > 0) {
      result++;
      B_X--;
    }
  }
  result += min(X_A, B_X);
  result += AB;
  cout << result << endl;
  return(0);
}