#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll n,a[22];
ll work(int l,int r,ll xl,ll xr){
	if (l>r) return 0;
	ll ans=1e18;
	for (int x=l;x<=r;x++)ans=min(ans,work(l,x-1,xl,xl+xr)+work(x+1,r,xl+xr,xr)+a[x]*(xl+xr));
	return ans;
}
int main(){
	cin>>n;
	for (int i=0;i<n;i++)cin>>a[i];
	cout<<a[0]+a[n-1]+work(1,n-2,1,1);
	return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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<bits/stdc++.h>
#define ll long long
using namespace std;
ll n,a[22];
ll work(int l,int r,ll xl,ll xr){
	if (l>r) return 0;
	ll ans=1e18;
	for (int x=l;x<=r;x++)ans=min(ans,work(l,x-1,xl,xl+xr)+work(x+1,r,xl+xr,xr)+a[x]*(xl+xr));
	return ans;
}
int main(){
	cin>>n;
	for (int i=0;i<n;i++)cin>>a[i];
	cout<<a[0]+a[n-1]+work(1,n-2,1,1);
	return 0;
}
```