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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var types = new int[3];
            var ans = 0;
            for (var i = 0; i < N; i++) {
                var s = Console.ReadLine();
                
                if (s[0] == 'B') {
                   if (s[s.Length-1] == 'A') {
                      types[2]++;
                   } else {
                      types[1]++;
                   }
                } else if (s[s.Length-1] == 'A') {
                   types[0]++;
                }
                
                var len = s.Length;
                s = s.Replace("AB", "");
                ans += (len-s.Length) / 2;
                
            }
            //Console.WriteLine(ans);
            //for(var i=0;i<3;i++) Console.WriteLine(types[i]);
            while (types[0] > 0 || types[1] > 0 || types[2] > 0) {
                if (types[0] > 0) {
                    types[0]--;
                    ans += Judge(types);
                } else if (types[2] > 0) {
                    types[2]--;
                    ans += Judge(types);
                } else {
                   types[1]--;
                }
            }
            
            Console.WriteLine(ans);
        }

        static int Judge(int[] t) {
            if (t[2] > 0) {
                t[2]--;
                t[0]++;
                return 1;
            } else if (t[1] > 0) {
                t[1]--;
                return 1;
            }
            
            return 0;
        }
    }
}