Problem:
Score : 700 points

Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3.
Let x_{i,j} defined as follows:

x_{1,j} := a_j \quad (1 \leq j \leq N)

x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

Constraints

2 \leq N \leq 10^6

a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N

Output

Print x_{N,1}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;
import java.util.HashMap;

public class Main{
  
  public void helpFunc(int N, int[] mat){
  	int val;
    for(int i=1; i<N; i++)
    {
      for(int j=0; j < N-i; j++)
      { 
        mat[j] = Math.abs(mat[j] - mat[j+1]);
        
      }
    }
    System.out.println(mat[0]);
  }
  
  static public void main(String args[])
  {
    Scanner sc= new Scanner(System.in);
    int N = sc.nextInt();
    int mat[] = new int[N];
    String s;
    s = sc.next();
    for(int j=0; j<N; j++)
    {
      mat[j] = s.charAt(j) - 48;
    }
    
    Main obj = new Main();
    obj.helpFunc(N, mat);
  }
}