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: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		char[] a = sc.next().toCharArray();
		sc.close();

		int[] x = new int[a.length - 1];
		boolean one = false;
		for ( int j = 0 ; j < a.length - 1 ; j++ ) {
			x[j] = Math.abs((int)a[j + 1] - (int)a[j]);
			if ( x[j] == 1 ) {
				one = true;
			}
		}

		int ans = 0;
		if ( one ) {
			int n = x.length - 1;
			boolean odd = false;
			for ( int r = 0 ; r < x.length ; r++ ) {
				if ( x[r] == 1 && n == ( n | (n - r)) ) {
					odd = !odd;
				}
			}
			ans = odd ? 1 : 0;
		} else {
			int n = x.length - 1;
			boolean odd = false;
			for ( int r = 0 ; r < x.length ; r++ ) {
				if ( x[r] == 2 && n == ( n | (n - r)) ) {
					odd = !odd;
				}
			}
			ans = odd ? 2 : 0;
		}
		System.out.println(ans);
	}
}