#include <bits/stdc++.h>
using namespace std;
const long long INF=(1LL<<50);
int n; 
long long a[30];
long long DFS(int l,int r,long long cntl,long long cntr){
	if(r-l<=1) return 0;
	long long ret=INF;
	for(int i=l+1;i<=r-1;++i)
		ret=min(ret,DFS(l,i,cntl,cntl+cntr)+DFS(i,r,cntl+cntr,cntr)+(cntl+cntr)*a[i]);
	return ret;	
}
int main(){
	
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
		scanf("%lld",&a[i]);
	printf("%lld\n",DFS(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;
const long long INF=(1LL<<50);
int n; 
long long a[30];
long long DFS(int l,int r,long long cntl,long long cntr){
	if(r-l<=1) return 0;
	long long ret=INF;
	for(int i=l+1;i<=r-1;++i)
		ret=min(ret,DFS(l,i,cntl,cntl+cntr)+DFS(i,r,cntl+cntr,cntr)+(cntl+cntr)*a[i]);
	return ret;	
}
int main(){
	
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
		scanf("%lld",&a[i]);
	printf("%lld\n",DFS(1,n,1,1)+a[1]+a[n]); 
	return 0;
}

```