Problem Statement

The shop supaisu-ya sells 2^N-1 kinds of spices: Spice $1, Spice 2, \ldots, Spice 2^N-1.$ One pack of each spice is in stock.
For each $i = 1, 2, \ldots, 2^N-1, Spice i costs c_i$ yen.
Takahashi can buy any of these spices.
He plans to make curry after getting home by choosing one or more of the bought spices and mixing them.
If $k spices, Spice A_1, Spice A_2, \ldots, Spice A_k$, are mixed, the hotness of the resulting curry is $A_1 \oplus A_2 \oplus \cdots \oplus A_k$, where $\oplus$ denotes the bitwise XOR.
Takahashi wants to decide the hotness of the curry based on his feeling after getting home. For now, he will buy a set of spices that allows him to make curry of any hotness from 1 through 2^N-1. Print the minimum possible amount of money Takahashi pays.

Input

Input is given from Standard Input in the following format:
N
$c_1 c_2 \ldots c_{2^N-1}$

Output

Print the minimum possible amount of money Takahashi pays.

Constraints

• $2 \leq N \leq 16$
• $1 \leq c_i \leq 10^9$
• All values in input are integers.

Sample Input 1

2
4 5 3

Sample Output 1

7

If Takahashi buys Spice 1 and 3, he can make curry of any hotness from 1 through 3, as follows.

• To make curry of hotness 1, use just Spice 1.
• To make curry of hotness 2, mix Spice 1 and Spice 3.
• To make curry of hotness 3, use just Spice 3.

Here, Takahashi pays c_1 + c_3 = 4 + 3 = 7 yen, which is the minimum possible amount he pays.

Sample Input 2

4
9 7 9 7 10 4 3 9 4 8 10 5 6 3 8

Sample Output 2

15

见题面 Input 部分

见题面 Output 部分