Add and Remove

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.

Examples

Input

4 3 1 4 2

Output

16

Input

6 5 2 4 1 6 9

Output

51

Input

10 3 1 4 1 5 9 2 6 5 3

Output

115

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

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

Examples

Input

4 3 1 4 2

Output

16

Input

6 5 2 4 1 6 9

Output

51

Input

10 3 1 4 1 5 9 2 6 5 3

Output

115

样例

10
3 1 4 1 5 9 2 6 5 3

115