#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
ll n,a[20];

ll ans(ll l,ll r,ll lx,ll rx){
  if(l+1==r) return 0;
  ll res=1e18;
  for(ll i=l+1;i<r;i++){
    res=min(res,a[i]*(lx+rx)+ans(l,i,lx,lx+rx)+ans(i,r,lx+rx,rx));
  }
  return res;
}

int main(){
  cin >> n;
  for(ll i=0;i<n;i++) cin >> a[i];
  cout << a[0]+a[n-1]+ans(0,n-1,1,1) << endl;
}
### 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 <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
ll n,a[20];

ll ans(ll l,ll r,ll lx,ll rx){
  if(l+1==r) return 0;
  ll res=1e18;
  for(ll i=l+1;i<r;i++){
    res=min(res,a[i]*(lx+rx)+ans(l,i,lx,lx+rx)+ans(i,r,lx+rx,rx));
  }
  return res;
}

int main(){
  cin >> n;
  for(ll i=0;i<n;i++) cin >> a[i];
  cout << a[0]+a[n-1]+ans(0,n-1,1,1) << endl;
}
```