#include<stdio.h>
#include<iostream>
#include<cstring>
#include<stdlib.h>
#include<time.h>
#include<math.h>
#include<algorithm>
#define ll long long
#define maxn 25
using namespace std;
int n;
ll a[maxn];

int read()
{
	int num,sign=1;
	char c;
	while((c=getchar())<'0'||c>'9')
		if(c=='-')sign=-1;
	num=c-'0';
	while((c=getchar())>='0'&&c<='9')
		num=(num<<1)+(num<<3)+c-'0';
	return num*sign;
}

ll dfs(int l,int r,int x,int y)
{
	if(l+1>=r)return 0;
	ll ans=1e17;
	for(register int i=l+1;i<r;++i)
		ans=min(ans,dfs(l,i,x,x+y)+dfs(i,r,x+y,y)+a[i]*(x+y));
	return ans;
}

int main()
{
	n=read();
	for(register int i=1;i<=n;++i)a[i]=read();
	cout<<a[1]+a[n]+dfs(1,n,1,1)<<endl;
	return 0;
}
### Prompt

Generate a cpp solution 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<stdio.h>
#include<iostream>
#include<cstring>
#include<stdlib.h>
#include<time.h>
#include<math.h>
#include<algorithm>
#define ll long long
#define maxn 25
using namespace std;
int n;
ll a[maxn];

int read()
{
	int num,sign=1;
	char c;
	while((c=getchar())<'0'||c>'9')
		if(c=='-')sign=-1;
	num=c-'0';
	while((c=getchar())>='0'&&c<='9')
		num=(num<<1)+(num<<3)+c-'0';
	return num*sign;
}

ll dfs(int l,int r,int x,int y)
{
	if(l+1>=r)return 0;
	ll ans=1e17;
	for(register int i=l+1;i<r;++i)
		ans=min(ans,dfs(l,i,x,x+y)+dfs(i,r,x+y,y)+a[i]*(x+y));
	return ans;
}

int main()
{
	n=read();
	for(register int i=1;i<=n;++i)a[i]=read();
	cout<<a[1]+a[n]+dfs(1,n,1,1)<<endl;
	return 0;
}
```