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.Text;
using System.Threading.Tasks;

namespace divertaPCBX
{
    class Program
    {
        static void Main(string[] args)
        {
            int AB = 0;
            int BA = 0;
            int BX = 0;
            int XA = 0;
            int N = int.Parse(Console.ReadLine());
            string[] s = new string[N];
            for (int i = 0; i < N; i++)
            {
                s[i] = Console.ReadLine();
                string tmp = s[i];
                while (s[i].IndexOf("AB") > -1)
                {
                    AB++;//"AB"
                    s[i] = s[i].Remove(s[i].IndexOf("AB"), 2);
                }
                s[i] = tmp;
                if (s[i].Substring(0, 1) == "B")
                {
                    if (s[i].Substring(s[i].Length - 1, 1) == "A")
                    {
                        BA++;//"BA"
                    }
                    else
                    {
                        BX++;//"BX"
                    }
                }
                else if (s[i].Substring(s[i].Length - 1, 1) == "A")
                {
                    XA++;//"XA"
                }
            }
            int ans;
            if (BA>0)
                if (XA > 0 && BX > 0)// XABABABABX
                {
                ans = AB+ BA+1+Math.Max(0,Math.Min(XA-1,BX-1));
                    //Console.WriteLine(AB+" "+(BA+1)+" "+Math.Max(0,Math.Min(XA-1,BX-1)));
                }
                else if ((XA>0&&BX==0)||(XA==0&&BX>0))// XABABA   BABABX
                {
                ans = AB+ BA+Math.Max(0,Math.Min(XA-1,BX-1));
                    //Console.WriteLine(AB+" "+BA+" "+Math.Max(0,Math.Min(XA-1,BX-1)));
                }
                else//BABABA
                {
                    ans = AB + BA - 1;
                }
            else//XABX
            {
                ans = AB + Math.Min(XA, BX);
            }           
            Console.WriteLine(ans);
        }
    }
}