#include <bits/stdc++.h>
using namespace std;
#define ref(i,x,y)for(int i=x;i<=y;++i)
#define def(i,x,y)for(int i=x;i>=y;--i)
#define pb push_back
#define SZ(x) ((int)x.size())
#define fi first
#define se second
#define mp make_pair
typedef long long LL;
const int N=19;
int n; LL val[N];
map<int,LL> a[N][N][2000];
LL solve(int x,int y,int sx,int sy){
	if(x==y||x+1==y)return 0;
	LL&res=a[x][y][sx][sy];
	if(res)return res-1;
	LL ans=1e18;
	ref(z,x+1,y-1){
		ans=min(ans,solve(x,z,sx,sx+sy)+solve(z,y,sx+sy,sy)+val[z]*(sx+sy));
	}
	res=ans+1;
	return ans;
}
int main(){
	cin>>n;
	ref(i,1,n)cin>>val[i];
	cout<<solve(1,n,1,1)+val[1]+val[n]<<endl;
}
### 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 <bits/stdc++.h>
using namespace std;
#define ref(i,x,y)for(int i=x;i<=y;++i)
#define def(i,x,y)for(int i=x;i>=y;--i)
#define pb push_back
#define SZ(x) ((int)x.size())
#define fi first
#define se second
#define mp make_pair
typedef long long LL;
const int N=19;
int n; LL val[N];
map<int,LL> a[N][N][2000];
LL solve(int x,int y,int sx,int sy){
	if(x==y||x+1==y)return 0;
	LL&res=a[x][y][sx][sy];
	if(res)return res-1;
	LL ans=1e18;
	ref(z,x+1,y-1){
		ans=min(ans,solve(x,z,sx,sx+sy)+solve(z,y,sx+sy,sy)+val[z]*(sx+sy));
	}
	res=ans+1;
	return ans;
}
int main(){
	cin>>n;
	ref(i,1,n)cin>>val[i];
	cout<<solve(1,n,1,1)+val[1]+val[n]<<endl;
}
```