#include<cstdio>
#include<iostream>
#define RI register int
#define CI const int&
using namespace std;
const int N=20;
int n,a[N];
inline long long DFS(CI l,CI r,CI cl,CI cr)
{
	if (r-l+1<=2) return 0; long long ret=1e18;
	for (RI i=l+1;i<r;++i) ret=min(ret,DFS(l,i,cl,cl+cr)+DFS(i,r,cl+cr,cr)+1LL*(cl+cr)*a[i]);
	return ret;
}
signed main()
{
	RI i; for (scanf("%d",&n),i=1;i<=n;++i)
	scanf("%d",&a[i]); return printf("%lld",DFS(1,n,1,1)+a[1]+a[n]),0;
}
### Prompt

Your task is to create 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<cstdio>
#include<iostream>
#define RI register int
#define CI const int&
using namespace std;
const int N=20;
int n,a[N];
inline long long DFS(CI l,CI r,CI cl,CI cr)
{
	if (r-l+1<=2) return 0; long long ret=1e18;
	for (RI i=l+1;i<r;++i) ret=min(ret,DFS(l,i,cl,cl+cr)+DFS(i,r,cl+cr,cr)+1LL*(cl+cr)*a[i]);
	return ret;
}
signed main()
{
	RI i; for (scanf("%d",&n),i=1;i<=n;++i)
	scanf("%d",&a[i]); return printf("%lld",DFS(1,n,1,1)+a[1]+a[n]),0;
}
```