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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var A = 0;
            var B = 0;
            var BA = 0;
            var AB = 0;
            for (int i = 0; i < N; i++)
            {
                var s = Read();
                var first = s[0];
                var last = s[s.Length - 1];
                if (first == 'B' && last == 'A') BA++;
                else if (first == 'B') B++;
                else if (last == 'A') A++;
                for (int j = 0; j < s.Length - 2; j++)
                {
                    if (s.Substring(j, 2) == "AB") AB++;
                }
            }
            if (N == 1)
            {
                Console.WriteLine(AB);
                return;
            }
            var ans = AB;
            var rem = 0;
            if(Math.Min(A, B) * 2 <= N)
            {
                ans += Math.Min(A, B);
                A -= Math.Min(A, B);
                B -= Math.Min(A, B);
                N -= Math.Min(A, B) * 2;
                rem = Math.Max(A, B);
            }
            else
            {
                ans += N / 2;
                A -= N / 2;
                B -= N / 2;
                N -= N / 2 * 2;
                rem = A + B;
            }
            
            if (rem > BA)
            {
                if (BA * 2 <= N) ans += BA;
                else ans += N / 2;
            }
            else
            {
                if (rem * 2 <= N)
                {
                    ans += rem;
                    BA -= rem;
                    N -= rem * 2;
                }
                else
                {
                    ans += N / 2;
                    BA -= N / 2;
                    N -= N / 2 * 2;
                }
                if (ans - AB != 0) ans += Math.Min(BA, N);
            }

            Console.WriteLine(ans);
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}