//
//  main.cpp
//  chalka
//
//  Created by Бахтияр on 16/11/19.
//  Copyright © 2019 Бахтияр. All rights reserved.
//

#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <unordered_map>
#include <iomanip>
#include <stack>
#include <queue>
#include <deque>
using namespace std;
int n,a[20];
 
long long dp(int l,int r,long long xl,long long xr) {
    if(l+1==r) return 0;
    long long ret=1e18;
    for(int i=l+1;i<r;i++) ret=min(ret,dp(l,i,xl,xl+xr)+dp(i,r,xl+xr,xr)+(xl+xr)*a[i]);
    return ret;
}
 
int main() {
    cin>>n;for(int i=1;i<=n;i++) cin>>a[i];
    cout<<dp(1,n,1,1)+a[1]+a[n];
    return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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
//
//  main.cpp
//  chalka
//
//  Created by Бахтияр on 16/11/19.
//  Copyright © 2019 Бахтияр. All rights reserved.
//

#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <unordered_map>
#include <iomanip>
#include <stack>
#include <queue>
#include <deque>
using namespace std;
int n,a[20];
 
long long dp(int l,int r,long long xl,long long xr) {
    if(l+1==r) return 0;
    long long ret=1e18;
    for(int i=l+1;i<r;i++) ret=min(ret,dp(l,i,xl,xl+xr)+dp(i,r,xl+xr,xr)+(xl+xr)*a[i]);
    return ret;
}
 
int main() {
    cin>>n;for(int i=1;i<=n;i++) cin>>a[i];
    cout<<dp(1,n,1,1)+a[1]+a[n];
    return 0;
}

```