#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 25;
int n,a[N];
ll ans;

ll dfs(int l,int r,int xl,int xr){
	if(l+1==r)return 0ll;
	ll ans=1e18;
	for(int mid=l+1;mid<r;mid++){
		ans=min(ans, dfs(l,mid,xl,xr+xl)+dfs(mid,r,xl+xr,xr)+1ll*(a[mid])*(xl+xr));
	}
	return ans;
}

int main()
{
	cin >> n;
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	cout << 1ll*a[1]+1ll*a[n]+dfs(1,n,1,1) << endl;
	return 0;
}
### 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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 25;
int n,a[N];
ll ans;

ll dfs(int l,int r,int xl,int xr){
	if(l+1==r)return 0ll;
	ll ans=1e18;
	for(int mid=l+1;mid<r;mid++){
		ans=min(ans, dfs(l,mid,xl,xr+xl)+dfs(mid,r,xl+xr,xr)+1ll*(a[mid])*(xl+xr));
	}
	return ans;
}

int main()
{
	cin >> n;
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	cout << 1ll*a[1]+1ll*a[n]+dfs(1,n,1,1) << endl;
	return 0;
}
```