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.

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.

Constraints

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

Sample Input 1

2
1 4 2 5

Sample Output 1

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.

Sample Input 2

2
3 1 5 4

Sample Output 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.

Sample Input 3

4
6 13 12 5 3 7 10 11 16 9 8 15 2 1 14 4

Sample Output 3

2

见题面 Input 部分

见题面 Output 部分