$2^N$ players, labeled $1$ through $2^N$, will compete against each other in a single-elimination programming tournament.  
The rating of Player $i$ is $A_i$. Any two players have different ratings, and a match between two players always results in the victory of the player with the higher rating.

The tournament looks like a perfect binary tree.  
Formally, the tournament will proceed as follows:

-   For each integer $i = 1, 2, 3, \dots, N$ in this order, the following happens.
    -   For each integer $j (1 \le j \le 2^{N - i})$, among the players who have never lost, the player with the $(2j - 1)$-th smallest label and the player with the $2j$-th smallest label play a match against each other.

Find the label of the player who will take **second place**, that is, lose in the final match.

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $A_3$ $\dots$ $A_{2^N}$
```

Print the label of the player who will take second place.

-   $1 \le N \le 16$
-   $1 \le A_i \le 10^9$
-   $A_i$ are pairwise different.
-   All values in input are integers.

2

First, there will be two matches between Players 1 and 2 and between Players 3 and 4. According to the ratings, Players 2 and 4 will win.
Then, there will be a match between Players 2 and 4, and the tournament will end with Player 4 becoming champion.
The player who will lose in the final match is Player 2, so we should print 2.

1

First, there will be two matches between Players 1 and 2 and between Players 3 and 4. According to the ratings, Players 1 and 3 will win.
Then, there will be a match between Players 1 and 3, and the tournament will end with Player 3 becoming champion.
The player who will lose in the final match is Player 1, so we should print 1.