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.Linq;
using System.Collections.Generic;
using System.Text;

namespace Program
{
    public class DIVERTA2019C
    {
        static public void Main(string[] args)
        {
            var N = NextInt;

            var fixABCount = 0;
            var s = new string[N];
            var lastAfirstBCount = 0;
            var lastACount = 0;
            var firstBCount = 0;
            for (int i = 0; i < N; ++i)
            {
                s[i] = NextString;
                for (int j = 0; j < s[i].Length - 1; ++j)
                {
                    if (s[i].Substring(j, 2) == "AB")
                    {
                        ++fixABCount;
                    }
                }
                var lastA = s[i].Last() == 'A';
                var firstB = s[i].First() == 'B';
                if (lastA && firstB)
                {
                    ++lastAfirstBCount;
                }
                else if (firstB)
                {
                    ++firstBCount;
                }
                else if (lastA)
                {
                    ++lastACount;
                }
            }

            Console.WriteLine(fixABCount + lastAfirstBCount - (lastAfirstBCount != 0 && lastACount == firstBCount ? 1 : 0) + Math.Min(lastACount, firstBCount));
        }

        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static int NextInt() => int.Parse(NextString());
            public static long NextLong() => long.Parse(NextString());
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => Console_.NextInt();
        static long NextLong => Console_.NextLong();
        static string NextString => Console_.NextString();

        static IEnumerable<int> Prime(int x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (int)(Math.Sqrt(x) / 2);
            for (int i = 1; i <= max; ++i)
            {
                if (!table[i])
                {
                    var add = 2 * i + 1;
                    yield return add;
                    for (int j = 2 * i * (i + 1); j <= halfx; j += add)
                    {
                        table[j] = true;
                    }
                }
            }
            for (int i = max + 1; i <= halfx; ++i)
            {
                if (!table[i]) yield return 2 * i + 1;
            }
        }
    }
}