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.*;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		String num = sc.next();
		List<List<Integer>> tocyu = new ArrayList<>();
		tocyu.add(new ArrayList<>());
		for (int i = 0; i < num.length(); i++) {
			tocyu.get(0).add(Integer.valueOf(num.charAt(i)));
		}

		for (int i = 1; i < n; i++) {
			tocyu.add(new ArrayList<>());
			for (int j = 1; j < tocyu.get(i-1).size(); j++) {
				tocyu.get(i).add(Math.abs(tocyu.get(i-1).get(j) - tocyu.get(i-1).get(j-1)));
			}
		}
		System.out.println(tocyu.get(n-1).get(0));
	}

}