#include <bits/stdc++.h>
using namespace std;
const int maxn = 18, maxm = 2600;
long long a[maxn];
map<tuple<int,int,int,int>, long long> f;
long long solve(int l, int r, int xl, int xr){
	if(l + 1 >=r) return 0;
	auto it = f.find(make_tuple(l, r, xl, xr));
	if(it != f.end()) return it->second;
	long long ans = 1ll<<60;
	for(int i = l + 1; i < r; i++){
		ans = min(ans, solve(l, i, xl, xl + xr) + solve(i, r, xl + xr, xr) + (xl + xr) * a[i]);
	}
	return f[make_tuple(l, r, xl, xr)] = ans;
}
int main(){
	int n; cin >> n;
	for(int i = 0; i < n; i++) cin >> a[i];
	cout << solve(0, n - 1, 1, 1) + a[0] + a[n - 1] << endl;
	return 0;
}

### Prompt

In cpp, your task is to solve 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;
const int maxn = 18, maxm = 2600;
long long a[maxn];
map<tuple<int,int,int,int>, long long> f;
long long solve(int l, int r, int xl, int xr){
	if(l + 1 >=r) return 0;
	auto it = f.find(make_tuple(l, r, xl, xr));
	if(it != f.end()) return it->second;
	long long ans = 1ll<<60;
	for(int i = l + 1; i < r; i++){
		ans = min(ans, solve(l, i, xl, xl + xr) + solve(i, r, xl + xr, xr) + (xl + xr) * a[i]);
	}
	return f[make_tuple(l, r, xl, xr)] = ans;
}
int main(){
	int n; cin >> n;
	for(int i = 0; i < n; i++) cin >> a[i];
	cout << solve(0, n - 1, 1, 1) + a[0] + a[n - 1] << endl;
	return 0;
}

```