//Just try and the idea will come
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll n,i,a[19];
ll go(ll l,ll r,ll x,ll y){
    if(r-l<2)return 0ll;
    ll res=1e18;
    for(ll i=l+1;i<r;i++)res=min(res,a[i]*(x+y)+go(l,i,x,y+x)+go(i,r,x+y,y));
    return res;
}
int main(){
    cin>>n;
    for(i=1;i<=n;i++)cin>>a[i];
    cout<<a[1]+a[n]+go(1,n,1,1);
}

### Prompt

Generate 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
//Just try and the idea will come
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll n,i,a[19];
ll go(ll l,ll r,ll x,ll y){
    if(r-l<2)return 0ll;
    ll res=1e18;
    for(ll i=l+1;i<r;i++)res=min(res,a[i]*(x+y)+go(l,i,x,y+x)+go(i,r,x+y,y));
    return res;
}
int main(){
    cin>>n;
    for(i=1;i<=n;i++)cin>>a[i];
    cout<<a[1]+a[n]+go(1,n,1,1);
}

```