Problem Statement

$2^N$ 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.

Constraints

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

Input

Input is given from Standard Input in the following format:

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

Output

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