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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Select(x => x - '0').ToArray();
        if (n < 10)
        {
            while (a.Length > 1)
            {
                a = Simulate(a);
            }
            Console.WriteLine(a[0]);
            return;
        }
        for (int i = 0; i < 5; i++)
        {
            a = Simulate(a);
        }
        int pow2 = 1;
        while (pow2 * 2 < a.Length) pow2 *= 2;
        var important = a.Length - pow2;
        var res = a.Take(important).Concat(a.Reverse().Take(important)).Sum() % 2;
        Console.WriteLine(res);
    }

    static int[] Simulate(int[] a)
    {
        return a.Zip(a.Skip(1), (x, y) => Abs(x - y)).ToArray();
    }
}