#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

template <typename _Tp> inline void IN(_Tp&x) {
	char ch;bool flag=0;x=0;
	while(ch=getchar(),!isdigit(ch)) if(ch=='-') flag=1;
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	if(flag) x=-x;
}

int n;ll a[25]; 
ll solve(int l,int r,ll x,ll y) {
	if(l>r) return 0;
	ll ans=1e18;
	for(int i=l;i<=r;++i)
		ans=min(ans,solve(l,i-1,x,x+y)+solve(i+1,r,x+y,y)+(x+y)*a[i]);
	return ans;
}
int main() {
	IN(n);
	for(int i=1;i<=n;++i) IN(a[i]);
	printf("%lld\n",a[1]+a[n]+solve(2,n-1,1,1));
	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 <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

template <typename _Tp> inline void IN(_Tp&x) {
	char ch;bool flag=0;x=0;
	while(ch=getchar(),!isdigit(ch)) if(ch=='-') flag=1;
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	if(flag) x=-x;
}

int n;ll a[25]; 
ll solve(int l,int r,ll x,ll y) {
	if(l>r) return 0;
	ll ans=1e18;
	for(int i=l;i<=r;++i)
		ans=min(ans,solve(l,i-1,x,x+y)+solve(i+1,r,x+y,y)+(x+y)*a[i]);
	return ans;
}
int main() {
	IN(n);
	for(int i=1;i<=n;++i) IN(a[i]);
	printf("%lld\n",a[1]+a[n]+solve(2,n-1,1,1));
	return 0;
}
```