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

class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());

        long ba = 0; // B**A
        long onlya = 0; // (B以外)**A
        long onlyb = 0; // B**(A以外)
        long ans = 0;
        for (int i = 0; i < n; i++)
        {
            string s = Console.ReadLine();
            if (s[0] == 'B' && s[s.Length - 1] == 'A') ba++;
            else if (s[0] == 'B') onlyb++;
            else if (s[s.Length - 1] == 'A') onlya++;
            for (int j = 0; j < s.Length - 1; j++)
            {
                if (s[j] == 'A' && s[j + 1] == 'B') ans++;
            }
        }

        // only同士くっつける
        ans += Math.Min(onlya, onlyb);
        // 余ったのをbaとくっつける
        long useba = Math.Min(ba, Math.Abs(onlya - onlyb));
        ans += useba;
        // 余ったba同士をくっつける
        if (Math.Abs(onlya - onlyb) > 0) ans += ba - useba;
        else if (ba > 0) ans += ba - 1;

        Console.WriteLine(ans);
    }
}