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.Scanner;
 
public class Main
{
	public static void main(String[] args)
    {
     	 Scanner scan = new Scanner(System.in);
      	int val = Integer.parseInt(scan.nextLine());
      	String[] words = scan.nextLine().split("");
      	int[] nums = new int[val];
      	for(int i = 0; i < val; i++)
        {
         	 nums[i] = Integer.parseInt(words[i]);
        }
      
      	for(int i = val - 1; i > 0; i--)
        {
          	int[] saveNum = new int[i];
         	for(int j = 0; j < i; j++)
            {
             	 saveNum[j] = Math.abs(nums[j] - nums[j + 1]);
            }
          	nums = saveNum;
        }
      
      	System.out.println(nums[0]);
    }
}