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.

Sample Input 1

4
3 1 4 2

Sample Output 1

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.

Sample Input 2

6
5 2 4 1 6 9

Sample Output 2

51

Sample Input 3

10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

115