#include <iostream>
#define ll long long
using namespace std;

ll a[20], mult[20];
ll solve(int left, int right){
	if(left+1==right) return 0;
	ll mn=(ll) 1e13;
	for(int i=left+1; i<right; ++i){
		mult[i]=mult[left]+mult[right];
		mn=min(mn, a[i]*mult[i]+solve(left, i)+solve(i, right));
		mult[i]=0;
	}
	return mn;
}


int main() {
	int N;
	cin >> N;
	for(int i=0; i<N; ++i) cin >> a[i];
	mult[0]=mult[N-1]=1;
	cout << a[0]+a[N-1]+solve(0, N-1) << endl;
	return 0;
}
### 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 <iostream>
#define ll long long
using namespace std;

ll a[20], mult[20];
ll solve(int left, int right){
	if(left+1==right) return 0;
	ll mn=(ll) 1e13;
	for(int i=left+1; i<right; ++i){
		mult[i]=mult[left]+mult[right];
		mn=min(mn, a[i]*mult[i]+solve(left, i)+solve(i, right));
		mult[i]=0;
	}
	return mn;
}


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