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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        String[] words = new String[N];
        for (int i = 0; i < N; i++) {
            words[i] = sc.next();
        }
        long A =  Arrays.stream(words).filter(s -> !s.startsWith("B") &&  s.endsWith("A")).count();
        long B =  Arrays.stream(words).filter(s ->  s.startsWith("B") && !s.endsWith("A")).count();
        long BA = Arrays.stream(words).filter(s ->  s.startsWith("B") &&  s.endsWith("A")).count();
        long containsAB = Arrays.stream(words).filter(s -> s.contains("AB")).count();

        long min = Math.min(A + BA, B + BA);

        if (A == 0 && B == 0 && BA > 0) {
            System.out.println(containsAB + BA - 1);
        } else {
            System.out.println(containsAB + min);
        }
    }
}