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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

class Program {
  static void Main(string[] args) {
    int n = int.Parse(Console.ReadLine());
    int ans = 0, hb = 0, ta = 0, ab = 0;
    
    for (int i = 0; i < n; i++) {
      var t = Console.ReadLine();

      for (int j = 0; j < t.Length - 1; j++) {
        if (t[j] == 'A' && t[j + 1] == 'B') {
          ans++;
        }
      }

      if (t[0] == 'B' && t[t.Length - 1] == 'A') {
        ab++;
      } else if (t[0] == 'B') {
        hb++;
      } else if (t[t.Length - 1] == 'A') {
        ta++;
      }
    }

    if (ab > 1) {
      ans += (ab - 1);
      ab = 1;
    }

    int m = Math.Min(hb, ta);
    ans += m;
    hb -= m;
    ta -= m;

    if (hb > 0 && ab == 1) {
      ans++;
    } else if (ta > 0 && ab == 1) {
      ans++;
    }

    Console.WriteLine(ans);
  }
}