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;
using System.Text.RegularExpressions;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var s = Console.In.ReadToEnd();

        var k = 0;
        for (int i = 1; i < s.Length; i++)
        {
            if (s[i - 1] != 'A' || s[i] != 'B')
            {
                continue;
            }

            k++;
        }
        var ss = s.Split('\n').Select(x => x.Trim()).Where(x => !string.IsNullOrEmpty(x)).ToArray();
        var prefixB = ss.Count(x => x.First() == 'B');
        var suffixA = ss.Count(x => x.Last() == 'A');
        var coexistence = ss.Count(x => x.First() == 'B' && x.Last() == 'A');
        var atBound = Math.Min(prefixB, suffixA);
        if (atBound == coexistence && prefixB == suffixA)
        {
            atBound--;
        }
        k += atBound;
        Console.WriteLine(k);
    }
}