#include <bits/stdc++.h>
#define fo(a,b,c) for (a=b; a<=c; a++)
#define fd(a,b,c) for (a=b; a>=c; a--)
#define min(a,b) (a<b?a:b)
#define ll long long
//#define file
using namespace std;

int n,i,j,k,l;
ll a[19];

ll dg(int l,int r,ll x,ll y)
{
	ll s,ans=9223372036854775807ll;
	int i;
	
	if (l>r) return 0;
	
	fo(i,l,r)
	{
		s=dg(l,i-1,x,x+y)+dg(i+1,r,x+y,y)+a[i]*(x+y);
		ans=min(ans,s);
	}
	return ans;
}

int main()
{
	#ifdef file
	freopen("agc035d.in","r",stdin);
	#endif
	
	scanf("%d",&n);
	fo(i,1,n) scanf("%lld",&a[i]);
	
	printf("%lld\n",dg(2,n-1,1,1)+a[1]+a[n]);
	
	fclose(stdin);
	fclose(stdout);
	return 0;
}
### Prompt

Please create a solution in cpp 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 <bits/stdc++.h>
#define fo(a,b,c) for (a=b; a<=c; a++)
#define fd(a,b,c) for (a=b; a>=c; a--)
#define min(a,b) (a<b?a:b)
#define ll long long
//#define file
using namespace std;

int n,i,j,k,l;
ll a[19];

ll dg(int l,int r,ll x,ll y)
{
	ll s,ans=9223372036854775807ll;
	int i;
	
	if (l>r) return 0;
	
	fo(i,l,r)
	{
		s=dg(l,i-1,x,x+y)+dg(i+1,r,x+y,y)+a[i]*(x+y);
		ans=min(ans,s);
	}
	return ans;
}

int main()
{
	#ifdef file
	freopen("agc035d.in","r",stdin);
	#endif
	
	scanf("%d",&n);
	fo(i,1,n) scanf("%lld",&a[i]);
	
	printf("%lld\n",dg(2,n-1,1,1)+a[1]+a[n]);
	
	fclose(stdin);
	fclose(stdout);
	return 0;
}
```