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 {
    public static void main(final String[] args) {
        final Scanner sc = new Scanner(System.in);

        final int N = sc.nextInt();
        final String A = sc.next();
        sc.close();
        int[][] n = new int[N][N];
        for (int i = 0; i < N; i++) {
            n[0][i] = A.charAt(i) - '0';
        }
        for (int i = 1; i < N; i++) {
            for (int j = 0; j < N; j++) {
                if(i + j < N){
                    n[i][j] = n[i - 1][j] - n[i - 1][j + 1];
                    if(n[i][j] < 0)
                        n[i][j] *= -1;
                }
            }
        }
        System.out.println(n[N - 1][0]);
    }
}