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;
using System.Text;
using System.Threading.Tasks;


namespace AtCoder
{
    class Pair
    {
        public Pair(long a,long b)
        {
            this.right = b;
            this.left = a;
        }
        public long right;
        public long left;
    }

    class Program
    {
        static void Main(string[] args)
        {
            new BG042().slove();
            #if DEBUG
                Console.WriteLine("続行するには何かキーを押してください．．．");
                Console.ReadLine();
            #endif

        }
    }

    class BG042
    {
        public void slove()
        {
            getLineInts();
            int[] input = getCharInts();
            if(input.Length < 2)
            {
                puts("0");
            }
            else
            {
                DoIt(input);
            }
        }

        public static void DoIt(int[] v)
        {
            var list = new int[v.Length - 1];
            int i;

            if (v.Length % 2 == 1)
            {
                for (i = 0; i < ((v.Length+1)/2); i++)
                {
                    if (i + 1 >= v.Length)
                    {
                        break;
                    }
                    list[i] = (Math.Abs(v[i + 1] - v[i]));
                    list[list.Length - i -1] = (Math.Abs(v[list.Length - i - 1]- Math.Abs(v[list.Length - i])));
                }
            }
            else
            {
                for (i = 0; i < (v.Length/2); i++)
                {
                    if (i + 1 >= v.Length)
                    {
                        break;
                    }
                    list[i] = (Math.Abs(v[i + 1] - v[i]));
                    list[list.Length - i - 1] = (Math.Abs(v[list.Length - i - 1] - Math.Abs(v[list.Length - i])));
                }
            }

            if(list.Length == 1)
            {
                Console.WriteLine(list[0]);
            }
            else
            {
                DoIt(list);
            }
        }

        public static int[] getCharInts()
        {
            //return getChar().Select(p => int.Parse(p.ToString())).ToArray();
            var a = new List<int>();
            var b = getChar();
            int i;
            for (i = 0; i < b.Count(); i++)
            {
                a.Add(int.Parse(b[i].ToString()));
            }
            return a.ToArray();
        }


        public static long[] getLineLongs()
        {
            return getLine().Select(p => long.Parse(p)).ToArray();
        }



        public static char[] getChar()
        {
            return getLine()[0].ToCharArray();
        }

        public static int[] getLineInts()
        {
            return getLine().Select(p => int.Parse(p)).ToArray();
        }

        public static String[] getLine()
        {
            String line = Console.ReadLine();
            String[] sp = line.Split(' ');
            if (sp.Length == 1)
            {
                //System.out.println(line);
                return new String[] { line };
            }
            else
            {
                return sp;
            }
        }
       

        void puts(Object mes)
        {
            Console.WriteLine(mes);
        }
    }


}