#include<iostream>
using namespace std;
#define ll long long
int n,A[20];
ll f(int l,int r,ll a,ll b){if(l>r)return 0;ll R=1e18;for(int m=l;m<=r;m++)R=min(R,f(l,m-1,a,a+b)+f(m+1,r,a+b,b)+A[m]*(a+b));return R;}
int main(){cin>>n;for(int i=1;i<=n;i++)cin>>A[i];cout<<A[1]+A[n]+f(2,n-1,1,1)<<endl;return 0;}
### Prompt

In CPP, your task is to solve the following problem:

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

### Response

```cpp
#include<iostream>
using namespace std;
#define ll long long
int n,A[20];
ll f(int l,int r,ll a,ll b){if(l>r)return 0;ll R=1e18;for(int m=l;m<=r;m++)R=min(R,f(l,m-1,a,a+b)+f(m+1,r,a+b,b)+A[m]*(a+b));return R;}
int main(){cin>>n;for(int i=1;i<=n;i++)cin>>A[i];cout<<A[1]+A[n]+f(2,n-1,1,1)<<endl;return 0;}
```