Score : $1000$ points

Problem Statement

There is a stack of $N$ cards, each of which has a non-negative integer written on it. The integer written on the $i$-th card from the top is $A_i$.

Snuke will repeat the following operation until two cards remain:

• Choose three consecutive cards from the stack.
• Eat the middle card of the three.
• For each of the other two cards, replace the integer written on it by the sum of that integer and the integer written on the card eaten.
• Return the two cards to the original position in the stack, without swapping them.

Find the minimum possible sum of the integers written on the last two cards remaining.

Constraints

• $2 \leq N \leq 18$
• $0 \leq A_i \leq 10^9 (1\leq i\leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_N$

Output

Print the minimum possible sum of the integers written on the last two cards remaining.

4
3 1 4 2

16

We can minimize the sum of the integers written on the last two cards remaining by doing as follows:

• Initially, the integers written on the cards are $3$, $1$, $4$, and $2$ from top to bottom.
• Choose the first, second, and third card from the top. Eat the second card with $1$ written on it, add $1$ to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now $4$, $5$, and $2$ from top to bottom.
• Choose the first, second, and third card from the top. Eat the second card with $5$ written on it, add $5$ to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now $9$ and $7$ from top to bottom.
• The sum of the integers written on the last two cards remaining is $16$.

6
5 2 4 1 6 9

51

10
3 1 4 1 5 9 2 6 5 3

115