#include <iostream>
#include <algorithm>
using namespace std;
#define int long long
#define R register
int a[20];
int n;
inline int dfs(int l,int r,int cl,int cr)
{
	if(r-l<2) return 0;
	int res=(1ll<<60);
	for(R int i=l+1;i<=r-1;i++)
		res=min(res,dfs(l,i,cl,cl+cr)+dfs(i,r,cl+cr,cr)+(cl+cr)*a[i]);
	return res;
}
signed main()
{
	cin>>n;
	for(R int i=1;i<=n;i++) cin>>a[i];
	cout<<dfs(1,n,1,1)+a[1]+a[n]<<endl;
}
### 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 <iostream>
#include <algorithm>
using namespace std;
#define int long long
#define R register
int a[20];
int n;
inline int dfs(int l,int r,int cl,int cr)
{
	if(r-l<2) return 0;
	int res=(1ll<<60);
	for(R int i=l+1;i<=r-1;i++)
		res=min(res,dfs(l,i,cl,cl+cr)+dfs(i,r,cl+cr,cr)+(cl+cr)*a[i]);
	return res;
}
signed main()
{
	cin>>n;
	for(R int i=1;i<=n;i++) cin>>a[i];
	cout<<dfs(1,n,1,1)+a[1]+a[n]<<endl;
}
```