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: Wrong Answer)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        String[] s=new String[4];
        for(int i=0;i<4;i++){
            s[i]="";
        }
        s[0]=sc.next();
        s[1]+=s[0].charAt(0);
        for(int i=1;i<n;i++){
            if(s[0].charAt(i-1)!=s[0].charAt(i)){
                s[1]+=s[0].charAt(i);
            }
        }
        for(int i=0;i<s[1].length()-1;i++){
            s[2]+=Integer.toString(Math.abs(s[1].charAt(i+1)-s[1].charAt(i)));
        }
        for(int i=1;i<s[2].length();i++){
            if(s[2].charAt(i-1)!=s[2].charAt(i)){
                s[3]+=s[2].charAt(i);
            }
        }
        if(s[3].length()==1){
            System.out.println(1);
        }else{
            System.out.println(0);
        }

    }

}