#include<iostream>
using namespace std;
typedef long long ll;
ll h[30],n;
const ll inf=1e18;
ll solve(int l,int r,ll a,ll b) {
    if(r-l<=1)return 0;
    ll ans=inf;
    for(int i=l+1;i<=r-1;i++) {
        ans=min(ans,solve(l,i,a,a+b)+solve(i,r,a+b,b)+h[i]*(a+b));
    }
    return ans;
    
}
int main() {
    cin>>n;for(int i=1;i<=n;i++)cin>>h[i];
    cout<<solve(1,n,1,1)+h[1]+h[n];
    return 0;
}//
### Prompt

Please create a solution in cpp to 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;
typedef long long ll;
ll h[30],n;
const ll inf=1e18;
ll solve(int l,int r,ll a,ll b) {
    if(r-l<=1)return 0;
    ll ans=inf;
    for(int i=l+1;i<=r-1;i++) {
        ans=min(ans,solve(l,i,a,a+b)+solve(i,r,a+b,b)+h[i]*(a+b));
    }
    return ans;
    
}
int main() {
    cin>>n;for(int i=1;i<=n;i++)cin>>h[i];
    cout<<solve(1,n,1,1)+h[1]+h[n];
    return 0;
}//
```