Problem:
Score : 100 points

Problem Statement

Kode Festival is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for "hardness".)

This year, 2^N stones participated. The hardness of the i-th stone is A_i.

In the contest, stones are thrown at each other in a knockout tournament.

When two stones with hardness X and Y are thrown at each other, the following will happen:

When X > Y:
The stone with hardness Y will be destroyed and eliminated.
The hardness of the stone with hardness X will become X-Y.

When X = Y:
One of the stones will be destroyed and eliminated.
The hardness of the other stone will remain the same.

When X < Y:
The stone with hardness X will be destroyed and eliminated.
The hardness of the stone with hardness Y will become Y-X.

The 2^N stones will fight in a knockout tournament as follows:

The following pairs will fight: (the 1-st stone versus the 2-nd stone), (the 3-rd stone versus the 4-th stone), ...

The following pairs will fight: (the winner of (1-st versus 2-nd) versus the winner of (3-rd versus 4-th)), (the winner of (5-th versus 6-th) versus the winner of (7-th versus 8-th)), ...

And so forth, until there is only one stone remaining.

Determine the eventual hardness of the last stone remaining.

Constraints

1 \leq N \leq 18

1 \leq A_i \leq 10^9

A_i is an integer.

Input

The input is given from Standard Input in the following format:

N
A_1
A_2
:
A_{2^N}

Output

Print the eventual hardness of the last stone remaining.

Sample Input 1

2
1
3
10
19

Sample Output 1

7

Sample Input 2

3
1
3
2
4
6
8
100
104

Sample Output 2

2

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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




namespace contest
{

    class contest
    {


        static void Main(string[] args)
        {


      


           
            int n = int.Parse(Console.ReadLine());
            int num = (int)Math.Pow(2,n);
            var stone = new int[num];
            for(int i=0; i<num; i++)
            {
                stone[i] = int.Parse(Console.ReadLine());
            }

            var cp = new List<int>(stone);
            
            var ans = new List<int>();
            while(true)
            {
                ans = new List<int>();
                for(int i=0; i<cp.Count(); i+=2)
                {
                    if (i == cp.Count() - 1) ans.Add(cp[i]);
                    else ans.Add(calc(cp[i], cp[i+1]));
                }
                cp = new List<int>(ans);

                if (ans.Count() == 1) break;
            }


            Console.WriteLine(ans[0]);



        }

		public static int calc(int a, int b)
        {
            if (a == b) return a;
            else if (a > b) return a - b;
            else return b - a;
        }
        

    }


   

    
}