#include <bits/stdc++.h>
using namespace std;
using ll = long long;

ll A[20];
ll f(int s, int e, int l, int r) {
	if (s > e) return 0;
	ll ret = 1ll << 62;
	for (int i = s; i <= e; ++i) ret = min(ret, f(s, i - 1, l, l + r) + f(i + 1, e, l + r, r) + (l + r) * A[i]);
	return ret;
}

int main() {
 	ios_base::sync_with_stdio(0), cin.tie(0);
 	int N; cin >> N;
 	for (int i = 1; i <= N; ++i) cin >> A[i];
	cout << f(2, N - 1, 1, 1) + A[1] + A[N];
	return 0;
}
### Prompt

Create a solution in CPP for 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 <bits/stdc++.h>
using namespace std;
using ll = long long;

ll A[20];
ll f(int s, int e, int l, int r) {
	if (s > e) return 0;
	ll ret = 1ll << 62;
	for (int i = s; i <= e; ++i) ret = min(ret, f(s, i - 1, l, l + r) + f(i + 1, e, l + r, r) + (l + r) * A[i]);
	return ret;
}

int main() {
 	ios_base::sync_with_stdio(0), cin.tie(0);
 	int N; cin >> N;
 	for (int i = 1; i <= N; ++i) cin >> A[i];
	cout << f(2, N - 1, 1, 1) + A[1] + A[N];
	return 0;
}
```