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:

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

2. 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)), ...

3. 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