#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL inf=0x3f3f3f3f3f3f3f3f;
const LL N=19;
LL n,a[N],t[N];
inline LL solve(LL l,LL r){
	if(l==r-1)return 0;
	LL ans=inf;
	for(LL i=l+1; i<r; ++i){
		t[i]=t[l]+t[r];
		ans=min(ans,solve(l,i)+solve(i,r)+t[i]*a[i]);
		t[i]=0;
	}
	return ans;
}
int main(){
	scanf("%lld",&n);
	for(LL i=1; i<=n; ++i)scanf("%lld",&a[i]);
	t[1]=t[n]=1;
	printf("%lld",a[1]+a[n]+solve(1,n));
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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>
using namespace std;
typedef long long LL;
const LL inf=0x3f3f3f3f3f3f3f3f;
const LL N=19;
LL n,a[N],t[N];
inline LL solve(LL l,LL r){
	if(l==r-1)return 0;
	LL ans=inf;
	for(LL i=l+1; i<r; ++i){
		t[i]=t[l]+t[r];
		ans=min(ans,solve(l,i)+solve(i,r)+t[i]*a[i]);
		t[i]=0;
	}
	return ans;
}
int main(){
	scanf("%lld",&n);
	for(LL i=1; i<=n; ++i)scanf("%lld",&a[i]);
	t[1]=t[n]=1;
	printf("%lld",a[1]+a[n]+solve(1,n));
	return 0;
}
```