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)

/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
I'm working for the day I will surpass you
https://www.a2oj.com/Ladder16.html
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class Main
   {
      public static void main(String omkar[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         int N = Integer.parseInt(infile.readLine());
         String input = infile.readLine();
         int[] arr = new int[N];
         for(int i=0; i < N; i++)
            arr[i] = Integer.parseInt(input.charAt(i)+"");
         ArrayList<Integer> ls = new ArrayList<Integer>();
         for(int x: arr)
            ls.add(x);
         while(ls.size() > 1)
         {
            ArrayList<Integer> temp = new ArrayList<Integer>();
            int last = -1;
            for(int i=0; i < ls.size()-1; i++)
            {
               int val = Math.abs(ls.get(i)-ls.get(i+1));
               if(val != last)
               {
                  temp.add(val);
                  last = val;
               }
            }
            ls = temp;
         }
         if(ls.size() > 0)
            System.out.println(ls.get(0));
         else
            System.out.println(0);
      }
   }