#include<iostream>
#define int long long
using namespace std;
const int N=20;
const int inf=1e18+2;
int ar[N];
int dp(int l,int r,int x1,int x2){
	if(r-l==1){
		return 0;
	}
	int i,now=inf;
	for(i=l+1;i<r;i++){
		now=min(now,dp(l,i,x1,x1+x2)+dp(i,r,x1+x2,x2)+(x1+x2)*ar[i]);
	}
	return now;
}
signed main(){
	int n,i,j,k,l;
	cin>>n;
	for(i=1;i<=n;i++){
		cin>>ar[i];
	}
	cout<<dp(1,n,1,1)+ar[1]+ar[n];
}
### 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>
#define int long long
using namespace std;
const int N=20;
const int inf=1e18+2;
int ar[N];
int dp(int l,int r,int x1,int x2){
	if(r-l==1){
		return 0;
	}
	int i,now=inf;
	for(i=l+1;i<r;i++){
		now=min(now,dp(l,i,x1,x1+x2)+dp(i,r,x1+x2,x2)+(x1+x2)*ar[i]);
	}
	return now;
}
signed main(){
	int n,i,j,k,l;
	cin>>n;
	for(i=1;i<=n;i++){
		cin>>ar[i];
	}
	cout<<dp(1,n,1,1)+ar[1]+ar[n];
}
```