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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;
using System.Numerics;

namespace SolutionCS
{
    class Program
    {
        class ELEMENT
        {
            public string str;
            public bool startIsB;
            public bool endIsA;
            public bool onlyA;
            public bool onlyB;
        }


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

            int startB = 0;
            int endA = 0;
            int bothBA = 0;

            int result = 0;

            for (int i = 0; i < N; i++)
            {
                ELEMENT e = new ELEMENT();
                string inStr = Console.ReadLine();

                char start = inStr[0];
                char end = inStr[inStr.Length - 1];

                if( start == 'B' && end == 'A')
                {
                    bothBA++;
                }
                else if ( start == 'B')
                {
                    startB++;
                }
                else if ( end == 'A')
                {
                    endA++;
                }

                int ind;
                do
                {
                    ind = inStr.IndexOf("AB");

                    if (ind >= 0)
                    {
                        inStr = inStr.Substring(ind + 2);
                        result++;
                    }
                }
                while (ind >= 0);
            }

            // 開始と終了が両方条件を満たすものは何も考えず接続
            if ( bothBA >= 2)
            {
                result += (bothBA - 1);
            }

            if ( bothBA > 0 && endA > 0)
            {
                result++;
                endA--;
            }
            if ( bothBA > 0 && startB > 0)
            {
                result++;
                startB--;
            }

            result += Math.Min(endA, startB);

            Console.WriteLine("{0}", result);
        }
    }
}