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;
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 = Enumerable.Range(0, items.Length).Select(x => CombinationCount(items.Length - 1, x, 2)).ToArray();
            var tmp = 0L;
            for (var i = 0; i < binCoef.Length; i++)
            {
                if (binCoef[i] % 2 == 1)
                {
                    if (items[i] % 2 == 1) tmp++;
                }
                else
                {
                    if (items[i] % 2 == 0) tmp--;
                }
            }
            return tmp % 2 == 1;
        }

        static long PermutationCount(long n, long k, long mod)
        {
            if (n < k) throw new ArgumentException();
            var result = 1L;
            for (var i = 0; i < k; i++)
                result = (result * (n - i) % mod) % mod;
            return result;
        }

        static long CombinationCount(long n, long k, long mod)
        {
            if (n < k) throw new ArgumentException();
            k = Math.Min(k, n - k);
            var top = PermutationCount(n, k, mod);
            var bottom = PermutationCount(k, k, mod);
            return (top * Power(bottom, mod - 2, mod)) % mod;
        }

        static long Power(long x, long y, long mod)
        {
            var result = 1L;
            while (y > 0)
            {
                if ((y & 1) == 1) result = ((result % mod) * (x % mod)) % mod;
                x = ((x % mod) * (x % mod)) % mod;
                y >>= 1;
            }
            return result;
        }
    }
}