#include <bits/stdc++.h>
#define int long long
#define f first
#define s second
#define inf 1e18+9
using namespace std;
const int N=20;
int a[N],n;
int f(int l,int r,int xl,int xr){
	if(r-l<=1)return 0;
	int res=inf;
	for(int i=l+1;i<r;i++){
		int x=f(l,i,xl,xl+xr)+f(i,r,xl+xr,xr)+(xl+xr)*a[i];
		res=min(res,x);
	}
	return res;
}
int32_t main(){
	if(fopen("input.txt", "r"))
	freopen("input.txt", "r", stdin),
	freopen("output.txt", "w", stdout);
	ios::sync_with_stdio(0),cin.tie(0);
	cin >> n;
	for(int i=0;i<n;i++)
		cin >> a[i];
	cout << f(0,n-1,1,1)+a[0]+a[n-1] << 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>
#define int long long
#define f first
#define s second
#define inf 1e18+9
using namespace std;
const int N=20;
int a[N],n;
int f(int l,int r,int xl,int xr){
	if(r-l<=1)return 0;
	int res=inf;
	for(int i=l+1;i<r;i++){
		int x=f(l,i,xl,xl+xr)+f(i,r,xl+xr,xr)+(xl+xr)*a[i];
		res=min(res,x);
	}
	return res;
}
int32_t main(){
	if(fopen("input.txt", "r"))
	freopen("input.txt", "r", stdin),
	freopen("output.txt", "w", stdout);
	ios::sync_with_stdio(0),cin.tie(0);
	cin >> n;
	for(int i=0;i<n;i++)
		cin >> a[i];
	cout << f(0,n-1,1,1)+a[0]+a[n-1] << endl;
}
```