# include<iostream>
# include<cstring>
# include<cstdio>
# include<cstdlib>
# include<algorithm>
# define LL long long
using namespace std;
int n,tot;
int a[300001],f[300001],g[300001];
int main()
{
	cin>>n;
	tot=1<<n;
	for(int i=0;i<tot;++i)
	  cin>>a[i];
	int ans=0;
	for(int i=1;i<tot;++i)
	  {
	  	for(int j=i;j>=0 ;j=(j-1)&i)
	  	  {
	  	  	if(f[i]<=a[j]) g[i]=f[i],f[i]=a[j];
	  	    else if(g[i]<a[j]) g[i]=a[j];
	  	    if(!j) break;
		  }
		ans=max(ans,f[i]+g[i]);
	  	printf("%d\n",ans);
	  }
}
### Prompt

Generate a cpp solution to the following problem:

There is an integer sequence of length 2^N: A_0, A_1, ..., A_{2^N-1}. (Note that the sequence is 0-indexed.)

For every integer K satisfying 1 \leq K \leq 2^N-1, solve the following problem:

* Let i and j be integers. Find the maximum value of A_i + A_j where 0 \leq i < j \leq 2^N-1 and (i or j) \leq K. Here, or denotes the bitwise OR.

Constraints

* 1 \leq N \leq 18
* 1 \leq A_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_0 A_1 ... A_{2^N-1}


Output

Print 2^N-1 lines. In the i-th line, print the answer of the problem above for K=i.

Examples

Input

2
1 2 3 1


Output

3
4
5


Input

3
10 71 84 33 6 47 23 25


Output

81
94
155
155
155
155
155


Input

4
75 26 45 72 81 47 97 97 2 2 25 82 84 17 56 32


Output

101
120
147
156
156
178
194
194
194
194
194
194
194
194
194

### Response

```cpp
# include<iostream>
# include<cstring>
# include<cstdio>
# include<cstdlib>
# include<algorithm>
# define LL long long
using namespace std;
int n,tot;
int a[300001],f[300001],g[300001];
int main()
{
	cin>>n;
	tot=1<<n;
	for(int i=0;i<tot;++i)
	  cin>>a[i];
	int ans=0;
	for(int i=1;i<tot;++i)
	  {
	  	for(int j=i;j>=0 ;j=(j-1)&i)
	  	  {
	  	  	if(f[i]<=a[j]) g[i]=f[i],f[i]=a[j];
	  	    else if(g[i]<a[j]) g[i]=a[j];
	  	    if(!j) break;
		  }
		ans=max(ans,f[i]+g[i]);
	  	printf("%d\n",ans);
	  }
}
```