#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>

int n;

int A[20];

long long DP(int l,int lx,int r,int rx){
	if (r-l==1) return 0;
	long long res=0x3f3f3f3f3f3f3f3f;
	for (int k=l+1;k<=r-1;k++)
		res=std::min(res,DP(l,lx,k,lx+rx)+DP(k,lx+rx,r,rx)+static_cast<long long>(A[k])*(lx+rx));
	return res;
}

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&A[i]);
	printf("%lld\n",DP(1,1,n,1)+A[1]+A[n]);
}

### 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<iostream>
#include<cstdio>
#include<cstring>
#include<vector>

int n;

int A[20];

long long DP(int l,int lx,int r,int rx){
	if (r-l==1) return 0;
	long long res=0x3f3f3f3f3f3f3f3f;
	for (int k=l+1;k<=r-1;k++)
		res=std::min(res,DP(l,lx,k,lx+rx)+DP(k,lx+rx,r,rx)+static_cast<long long>(A[k])*(lx+rx));
	return res;
}

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&A[i]);
	printf("%lld\n",DP(1,1,n,1)+A[1]+A[n]);
}

```