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 atcorder.DataStructure;
namespace atcorder
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            atcorder.Test.Run();
        }
    }


    public class Test
    {
        public static void Run()
        {
            int AB_num = 0;
            int Aend_num = 0;
            int Bstart_num = 0;
            int AB_both_num = 0;
            int N = int.Parse(Console.ReadLine());
            List<string> strings = new List<string>();
            for (int i = 0; i < N;i++){
                string s = Console.ReadLine();
                int pos = 0;
                while(true){
                    pos = s.IndexOf("AB",pos);
                    if (pos == -1) break;
                    AB_num++;
                    pos++;
                }
                if (s[0] == 'B' && s[s.Length-1]!='A') Bstart_num++;
                if (s[0] != 'B' && s[s.Length - 1] == 'A') Aend_num++;
                if (s[0] == 'B' && s[s.Length - 1] == 'A') AB_both_num++;
            }
            int result=AB_num;
            if(Aend_num >0&&Bstart_num>0){
                result += AB_both_num + 1;
                Aend_num--;Bstart_num--;
                result += Math.Min(Aend_num, Bstart_num);
            }else{
                result += AB_both_num;
            }
            Console.WriteLine(result);
        }
    }




    public class Input
    {
        int arg;
        int length;
        string s;
        string[] ss;
        char sep;
        public Input(char _sep = ' ')
        {
            sep = _sep;
        }
        public void ReadLine()
        {
            s = Console.ReadLine();
            if (sep != '\0') ss = s.Split(sep);
            else
            {
                ss = new string[1];
                ss[0] = s;
            }
            arg = 0;
            length = ss.Length;
        }
        public T Next<T>()
        {
            if (arg == length) throw new IndexOutOfRangeException();
            return (T)Convert.ChangeType(ss[arg++], typeof(T));
        }
        public void SetSeparater(char _sep)
        {
            sep = _sep;
        }
    }
}