#include<bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int,int> pii;

const int inf=0x3f3f3f3f;
const LL Linf=1ll<<61;

int n,a[20];

map<pii,LL> dp[20][20];
LL dfs(int l,int r,int tl,int tr)
{
	if(l==r-1)return 0;
	if(dp[l][r].find(mp(tl,tr))!=dp[l][r].end())return dp[l][r][mp(tl,tr)];
	LL ret=Linf;
	for(int m=l+1;m<r;m++)ret=min(ret,dfs(l,m,tl,tl+tr)+dfs(m,r,tl+tr,tr)+(LL)(tl+tr)*a[m]);
	return (dp[l][r][mp(tl,tr)]=ret);
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",a+i);
	printf("%lld\n",dfs(1,n,1,1)+a[1]+a[n]);
	return 0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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;
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int,int> pii;

const int inf=0x3f3f3f3f;
const LL Linf=1ll<<61;

int n,a[20];

map<pii,LL> dp[20][20];
LL dfs(int l,int r,int tl,int tr)
{
	if(l==r-1)return 0;
	if(dp[l][r].find(mp(tl,tr))!=dp[l][r].end())return dp[l][r][mp(tl,tr)];
	LL ret=Linf;
	for(int m=l+1;m<r;m++)ret=min(ret,dfs(l,m,tl,tl+tr)+dfs(m,r,tl+tr,tr)+(LL)(tl+tr)*a[m]);
	return (dp[l][r][mp(tl,tr)]=ret);
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",a+i);
	printf("%lld\n",dfs(1,n,1,1)+a[1]+a[n]);
	return 0;
}
```