#include <bits/stdc++.h>

#define int long long

using namespace std;

int n, a[233];

int dfs(int l, int r, int xl, int xr) {
	if (l + 1 == r) return 0;
	int ans = 1e18;
	for (int m = l + 1; m <= r - 1; m++) 
		ans = min(ans, dfs(l, m, xl, xl + xr) + dfs(m, r, xl + xr, xr) + (xl + xr) * a[m]);
	return ans;
}		

signed main(void) {
	cin >> n;
	for (int i = 1; i <= n; i++) cin >> a[i];
	cout << dfs(1, n, 1, 1) + a[1] + a[n] << "\n";
}

### Prompt

Please formulate 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 <bits/stdc++.h>

#define int long long

using namespace std;

int n, a[233];

int dfs(int l, int r, int xl, int xr) {
	if (l + 1 == r) return 0;
	int ans = 1e18;
	for (int m = l + 1; m <= r - 1; m++) 
		ans = min(ans, dfs(l, m, xl, xl + xr) + dfs(m, r, xl + xr, xr) + (xl + xr) * a[m]);
	return ans;
}		

signed main(void) {
	cin >> n;
	for (int i = 1; i <= n; i++) cin >> a[i];
	cout << dfs(1, n, 1, 1) + a[1] + a[n] << "\n";
}

```