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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		String s = br.readLine();
		List<Integer> list = new ArrayList<>(n);
		for (int i = 0; i < n; i++) {
			list.add(s.charAt(i) - '0');
		}
		br.close();

		int f = -1;
		for (int i = 1; i < n; i++) {
			if (list.get(i) == 1) {
				f = i;
				break;
			}
		}
		int r = n;
		for (int i = n - 2; i >= 0; i--) {
			if (list.get(i) == 1) {
				r = i;
				break;
			}
		}
		if (f <= 0 && n - 1 <= r) {
			List<Integer> work = new ArrayList<>(list.size());
			for (int i = 0; i < f; i++) {
				work.add(list.get(i));
			}
			work.add(1);
			work.add(1);
			for (int i = r + 1; i < n; i++) {
				work.add(list.get(i));
			}
			list = work;
		}

		while (list.size() > 1) {
			List<Integer> work = new ArrayList<>(list.size());
			int now = -1;
			int cnt = 0;
			for (int i = 1; i < list.size(); i++) {
				int val = Math.abs(list.get(i - 1) - list.get(i));
				if (val == now) {
					cnt++;
				} else {
					if (cnt > 0) {
						work.add(now);
						if (now > 0 && cnt > 1) {
							work.add(now);
						}
					}
					now = val;
					cnt = 1;
				}
			}
			work.add(now);
			if (now > 0 && cnt > 1) {
				work.add(now);
			}
			list = work;
		}
		System.out.println(list.get(0));
	}
}