p02978 AtCoder Grand Contest 035 - 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
```python
#YouTube
import sys
sys.setrecursionlimit(10**6)

def kukan(l,r,el=1,er=1):
    em=el+er
    if l+1==r:
        return 0
    if l+2==r:
        return a[l+1]*em
    t=(l,r,el,er)
    if t in memo:
        return memo[t]
    re=10**11
    for m in range(l+1,r):
        tmp=kukan(l,m,el,em)+kukan(m,r,em,er)+a[m]*em
        if tmp<re:
            re=tmp
    memo[t]=re
    return re

n=int(input())
a=list(map(int,input().split()))
memo={}
print(a[0]+kukan(0,n-1)+a[-1])
```