#include<bits/stdc++.h>
using namespace std;
#define int long long
int a[20];
int f(int l,int r,int cl,int cr){
	int ans=1e18;
	if(l+1>=r) return 0;
	for(int i=l+1;i<=r-1;++i)
		ans=min(ans,f(l,i,cl,cl+cr)+f(i,r,cl+cr,cr)+a[i]*(cl+cr));
	return ans;
}
signed main(){
	int n;
	cin>>n;
	for(int i=1;i<=n;++i)
		cin>>a[i];
	cout<<f(1,n,1,1)+a[1]+a[n];
	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>
using namespace std;
#define int long long
int a[20];
int f(int l,int r,int cl,int cr){
	int ans=1e18;
	if(l+1>=r) return 0;
	for(int i=l+1;i<=r-1;++i)
		ans=min(ans,f(l,i,cl,cl+cr)+f(i,r,cl+cr,cr)+a[i]*(cl+cr));
	return ans;
}
signed main(){
	int n;
	cin>>n;
	for(int i=1;i<=n;++i)
		cin>>a[i];
	cout<<f(1,n,1,1)+a[1]+a[n];
	return 0;
}

```