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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace B
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var n = int.Parse(Console.ReadLine());
            var ai = Console.ReadLine().Trim().Select(x => x - '1').ToArray();
            var isContain1 = ai.Contains(1);
            if (!isContain1) ai = ai.Select(x => x /= 2).ToArray();
            var isOdd = IsOdd(ai);

            if (isContain1) Console.WriteLine(isOdd ? 1 : 0);
            else Console.WriteLine(isOdd ? 2 : 0);
        }

        static bool IsOdd(int[] items)
        {
            var binCoef = new int[items.Length];
            var n = items.Length - 1;
            for (int i = 0, j = binCoef.Length - 1; i < j; i++, j--)
            {
                binCoef[i] = binCoef[j] = n == (i | (n - i)) ? 1 : 0;
            }

            var t = 0;
            for (var i = 0; i < binCoef.Length; i++)
            {
                if (binCoef[i] % 2 == 1)
                {
                    if (items[i] % 2 == 1) t++;
                }
            }
            return t % 2 == 1;
        }
    }
}