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;

namespace diverta2019_c
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var SD = new Dictionary<string, int>();

            // Aで終わる
            SD.Add("01", 0);

            // Bで始まる
            SD.Add("10", 0);

            // Bで始まりAで終わる
            SD.Add("11", 0);

            int r = 0;

            for (int i = 0; i < N; i++) 
            {
                var s = Console.ReadLine();
                int m = 0;

                if (s.Contains("AB"))
                    for (int j = 0; j < s.Length - 1; j++)
                        if (s[j] == 'A' && s[j + 1] == 'B')
                            r++;

                if (s[0] == 'B')
                    m += 10;

                if (s[s.Length - 1] == 'A')
                    m += 1;

                if (m > 0) 
                    SD[m.ToString("00")]++;
            }

            //「Aで終わる」x1「Bで始まりAで終わる」xN「Bで始まる」x1
            if (SD["01"] > 0 && SD["11"] > 0 && SD["10"] > 0)
            {
                SD["01"]--;
                SD["10"]--;
                r += SD["11"] + 1;
            }
            //「Bで始まりAで終わる」xN「Bで始まる」x1
            else if (SD["11"] > 0 && SD["10"] > 0)
            {
                SD["10"]--;
                r += SD["11"] ;
            }

            //「Aで終わる」と「Bで始まる」を可能な限りつなげる
            r += Math.Min(SD["01"], SD["10"]);

            Console.WriteLine(r);
        }
    }
}