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.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.AGC_043
{
    class B
    {

        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            string s = Read();
            int[] array = new int[n];
            bool hasOne = false;
            for(int i = 0; i < n; i++)
            {
                array[i] = s[i] - '1';
                if (array[i] == 1)
                {
                    hasOne = true;
                }
            }
            if (!hasOne)
            {
                for(int i = 0; i < n; i++)
                {
                    array[i] /= 2;
                }
            }

            bool isOdd = IsOdd(array);

            if (isOdd)
            {
                if (hasOne)
                {
                    WriteLine(1);
                }
                else
                {
                    WriteLine(2);
                }
            }
            else
            {
                WriteLine(0);
            }
        }

        static bool IsOdd(int[] array)
        {
            bool[] oddArray = CalcOddArray(array.Length);
            int cnt = 0;
            for(int i = 0; i < array.Length; i++)
            {
                if (array[i] == 1&&oddArray[i])
                {
                    cnt++;                    
                }
            }

            return cnt % 2 == 1;
        }

        static bool[] CalcOddArray(int n)
        {
            bool[] array = new bool[n];
            array[0] = true;
            int numeratorCnt = 0;
            int denominatorCnt = 0;
            for (int i = 1; i < n; i++) {
                int numerator = n - i;
                int denominator = i;

                while (numerator % 2 == 0)
                {
                    numeratorCnt++;
                    numerator /= 2;
                }

                while (denominator % 2 == 0)
                {
                    denominatorCnt++;
                    denominator /= 2;
                }

                array[i] = numeratorCnt == denominatorCnt;
            }

            return array;
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}