#include<cstdio>
using namespace std;
long long n,v[19],ct;
long long Min(long long a,long long b){return a<b?a:b;}
long long DP(int l,int r,int s1,int s2)
{
	if(l+1==r)return v[l]*s1+v[r]*s2;
	long long as=2e18;
	for(int i=l+1;i<r;i++)as=Min(as,DP(l,i,s1,s1+s2)+DP(i,r,s1+s2,s2)-v[i]*(s1+s2));
	return as;
}
int main(){scanf("%lld",&n);for(int i=1;i<=n;i++)scanf("%lld",&v[i]);printf("%lld\n",DP(1,n,1,1));}//
### Prompt

Please formulate 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>
using namespace std;
long long n,v[19],ct;
long long Min(long long a,long long b){return a<b?a:b;}
long long DP(int l,int r,int s1,int s2)
{
	if(l+1==r)return v[l]*s1+v[r]*s2;
	long long as=2e18;
	for(int i=l+1;i<r;i++)as=Min(as,DP(l,i,s1,s1+s2)+DP(i,r,s1+s2,s2)-v[i]*(s1+s2));
	return as;
}
int main(){scanf("%lld",&n);for(int i=1;i<=n;i++)scanf("%lld",&v[i]);printf("%lld\n",DP(1,n,1,1));}//
```