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: Runtime Error)

import java.util.*;
public class Main
{
  private int absdiff(int a,int b)
  {
    return (a>b?a-b:b-a);
  }
  public static void main(String args[])
  {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    sc.nextLine();
    int arr[][]=new int[n][];
    for(int i=0;i<n;i++)
    {
      arr[i]=new int[n-i];
      arr[i][0]=sc.nextInt();
    }
    Main ob=new Main();
    for(int j=1;j<n;j++)
    {
      for(int i=0;i<(n-j);j++)
      {
        arr[i][j]=ob.absdiff(arr[i][j-1],arr[i+1][j-1]);
      }
    }
    System.out.println(arr[0][n-1]);
  }
}