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 static System.Math;

class Program{
    static int a = 0;
    static int b = 0;
    static int c = 0;

    static void Main(){
        int n = int.Parse(Console.ReadLine());
        string[] s = new string[n];
        for (int i = 0;i < n;i++) s[i] = Console.ReadLine();

        int ans = 0;
        foreach (var si in s) ans += Count(si);

        ans += Min(a,b);
        int l = Abs(a - b);
        if (l == 0){
            ans += Max(0,c - 1);
            goto END;
        }
        ans += Min(l,c) + Max(0,c-l);
    
        END:
        Console.WriteLine(ans);
    }

    static int Count(string s){
        int n = s.Length;
        if (s[0] != 'B' && s[n - 1] == 'A') a++;
        if (s[0] == 'B' && s[n - 1] != 'A') b++;
        if (s[0] == 'B' && s[n - 1] == 'A') c++;
        int v = 0;
        for (int i = 0;i < n - 1;i++)
            if (s[i] == 'A' && s[i + 1] == 'B')
                v++;
        return v;
    }
}