7349: ABC236 —— F - Spices
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Description
The shop supaisu-ya sells $2^N-1$ kinds of spices: Spice 1, Spice 2, …, 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.
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:
$N$
$c_1\ c_2\ \ldots\ c_{2^N-1}$
$N$
$c_1\ c_2\ \ldots\ c_{2^N-1}$
Output
Print the minimum possible amount of money Takahashi pays.
Constraints
$2≤N≤16$
$1 \leq c_i \leq 10^9$
All values in input are integers.
$1 \leq c_i \leq 10^9$
All values in input are integers.
Sample 1 Input
2
4 5 3
Sample 1 Output
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 2 Input
4
9 7 9 7 10 4 3 9 4 8 10 5 6 3 8
Sample 2 Output
15