#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll n,a[101];
ll dfs(ll l,ll r,ll x,ll y){
	if(l+1==r)return 0;
	ll i,ans=1e18,xlh=x+y;
	for(i=l+1;i<r;i++)ans=min(ans,dfs(l,i,x,xlh)+dfs(i,r,xlh,y)+xlh*a[i]);
	return ans;
}
int main(){
	ll i;
	scanf("%lld",&n);
	for(i=1;i<=n;i++)scanf("%lld",&a[i]);
	printf("%lld",dfs(1,n,1,1)+a[1]+a[n]);
}
/*
发现是道较简单题 
*/
### 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<bits/stdc++.h>
#define ll long long
using namespace std;
ll n,a[101];
ll dfs(ll l,ll r,ll x,ll y){
	if(l+1==r)return 0;
	ll i,ans=1e18,xlh=x+y;
	for(i=l+1;i<r;i++)ans=min(ans,dfs(l,i,x,xlh)+dfs(i,r,xlh,y)+xlh*a[i]);
	return ans;
}
int main(){
	ll i;
	scanf("%lld",&n);
	for(i=1;i<=n;i++)scanf("%lld",&a[i]);
	printf("%lld",dfs(1,n,1,1)+a[1]+a[n]);
}
/*
发现是道较简单题 
*/
```