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: Time Limit Exceeded)

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

class Progaram
{
    static int Seek(List<int> blist, int n)
    {
        var alist = new List<int>();
        var bnum = blist[0];
        int anum;
        for (var i = 1; n > i; i++)
        {
            anum = blist[i];
            alist.Add(Math.Abs(bnum - anum));
            bnum = anum;
        }
        int ans = 0;
        if (alist.Count != 1) ans = Seek(alist, alist.Count);
        else ans = alist[0];
        return ans;
    }

    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var nums = Console.ReadLine().ToCharArray()
            .Select(x => (int)x).ToList();
        Console.WriteLine(Seek(nums, n));
    }
}