#include<bits/stdc++.h>
#define REP(i,x,y) for(ll i=x; i<=y; i++)
#define vll vector<ll>
using namespace std;
typedef long long ll;
ll const MAX = 1e5 + 5;

vll a(30);

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

int main(){
	ll n;
	cin >> n;
	REP(i,1,n){
		cin >> a[i];
	}
	cout << f(1,1,n,1) + a[1] + a[n] << endl; 
}
### 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<bits/stdc++.h>
#define REP(i,x,y) for(ll i=x; i<=y; i++)
#define vll vector<ll>
using namespace std;
typedef long long ll;
ll const MAX = 1e5 + 5;

vll a(30);

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

int main(){
	ll n;
	cin >> n;
	REP(i,1,n){
		cin >> a[i];
	}
	cout << f(1,1,n,1) + a[1] + a[n] << endl; 
}
```