#D90. Kode Festival
Kode Festival
Kode Festival
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:
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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.
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When X = Y: One of the stones will be destroyed and eliminated. The hardness of the other stone will remain the same.
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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:
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The following pairs will fight: (the 1-st stone versus the 2-nd stone), (the 3-rd stone versus the 4-th stone), ...
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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)), ...
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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.
Examples
Input
2 1 3 10 19
Output
7
Input
3 1 3 2 4 6 8 100 104
Output
2
inputFormat
Input
The input is given from Standard Input in the following format:
N A_1 A_2 : A_{2^N}
outputFormat
Output
Print the eventual hardness of the last stone remaining.
Examples
Input
2 1 3 10 19
Output
7
Input
3 1 3 2 4 6 8 100 104
Output
2
样例
3
1
3
2
4
6
8
100
1042