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: Runtime Error)

import java.util.*;

public class Main{
  public static void main(String[]args){
    Scanner sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.nextLine());
    int[] inf = new int[N+1];
    int now = 0;
    int paint = 1;
    int[] ans = new int[N-1];
    int max = 0;
    int[][] val = new int[N-1][4];
    for(int i = 0; i < N-1; i++){
      String[] S = sc.nextLine().split(" ");
      val[i][0] = Integer.parseInt(S[0]);
      val[i][1] = Integer.parseInt(S[1]);
      val[i][2] = i;
    }
    Arrays.sort(val, (a,b)->Integer.compare(a[0],b[0]));
    
    for(int i = 0; i < N-1; i++){
      int a = val[i][0];
      int b = val[i][1];
      if(i == 0){
        now = a;
      }else{
        if(a == now){
          paint++;
        }else{
          now = a;
          paint = 1;
        }
        if(inf[a] == paint){
          paint++;
        }
      }
      val[i][3] = paint;
      inf[b] = paint;
      if(max < paint){
        max = paint;
      }
    }
    
    Arrays.sort(val, (a,b)->Integer.compare(a[2],b[2]));
    System.out.println(max);
    for(int i = 0; i < N-1; i++){
      System.out.println(val[i][3]);
    }
  }
}