#include <cstdio>
#include <iostream>

using namespace std;

long long a[25] , n;

#define ll long long

ll f(ll l , ll r , ll x , ll y){
	ll  ans = 1e18;
    if(r - l <= 1) 
        return 0;
    for(int i = l + 1; i <= r - 1; i++)
        ans = min((f(l, i, x, x + y) + f(i, r, x + y, y) + a[i] * (x + y)), ans);
    return ans;
}

int main(){
	cin >> n;
	for(int i = 1; i <= n; i++)
		cin >> a[i];
	cout << a[1] + a[n] + f(1 , n , 1 , 1) << endl;
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 <cstdio>
#include <iostream>

using namespace std;

long long a[25] , n;

#define ll long long

ll f(ll l , ll r , ll x , ll y){
	ll  ans = 1e18;
    if(r - l <= 1) 
        return 0;
    for(int i = l + 1; i <= r - 1; i++)
        ans = min((f(l, i, x, x + y) + f(i, r, x + y, y) + a[i] * (x + y)), ans);
    return ans;
}

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