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.Linq;
    using System.Collections.Generic;
    using System.Text.RegularExpressions;
    using System.Text;
     
    public class Program
    {
        public void Proc() {
            Reader.IsDebug = false;
            int inpt = int.Parse(Reader.ReadLine());

            long itemCount = ((long)1<<inpt);

            List<long> items = new List<long>();

            for(int i=0; i<itemCount; i++) {
                items.Add(long.Parse(Reader.ReadLine()));
            }

            long ans = GetInt(items);
            Console.WriteLine(ans);
        }

        private long GetInt(List<long> items) {
            List<long> list = items;
            while(list.Count > 1) {
                List<long> tmp = new List<long>();

                for(int i=0; i<list.Count; i+=2) {
                    long koudo = Math.Abs(list[i] - list[i+1]);
                    if(koudo == 0) {
                        tmp.Add(list[i]);
                    } else {
                        tmp.Add(koudo);
                    }
                }
                list = tmp;
            }
            return list[0];  
        }


        public class Reader {
            public static bool IsDebug = true;
            private static System.IO.StringReader SReader;
            private static string InitText = @"







";
            public static string ReadLine() {
                if(IsDebug) {
                    if(SReader == null) {
                        SReader = new System.IO.StringReader(InitText.Trim());
                    }
                    return SReader.ReadLine();
                } else {
                    return Console.ReadLine();
                }
            }
        }
        public static void Main(string[] args)
        {
            Program prg = new Program();
            prg.Proc();
        }
    }