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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program kode_festival
  implicit none
  integer :: n , a(262144), b(131072), m, i, k
  a = 0
  b = 0
  read(*,*) n
  m = 2**n
  do i = 1, m
    read(*,*) a(i)
  end do
  do k = 1, n
    m = m/2
    do i = 1, m
      if (a(2*i-1).eq.a(2*i)) then
        b(i) = a(2*i-1)
      else
        b(i) = max(a(2*i-1),a(2*i))-min(a(2*i-1),a(2*i))
      end if
    end do
    a(1:m) = b(1:m)
  end do
  write(*,'(i0)') a(1)
  stop
end program kode_festival