#include<bits/stdc++.h>

using namespace std;

const int MAXN=1000010;

int cnt=0,G[100];

void Insertion_Sort(int s,int t,int n,int* A)
{
	for(int i=s+t;i<n;i+=t)
	{
		int key=A[i],j=i-t;
		while(j>=0&&A[j]>key)
		{
			A[j+t]=A[j];
			j-=t;
			cnt++;
		}
		if(A[j+t]!=key)
		{
			A[j+t]=key;
			//cnt++;
		}
	}
}

int main()
{
	for(int i=0;(G[i]=G[i-1]*3+1)<=MAXN;i++);
	static int n,A[MAXN];
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%d",&A[i]);
	int t;
	for(t=0;G[t]<=n;t++);
	printf("%d\n",t);
	for(int i=t-1;i>=0;i--)
		printf("%d%c",G[i],i==0?'\n':' ');
	for(int i=t-1;i>=0;i--)
		for(int j=0;j<G[i];j++)
			Insertion_Sort(j,G[i],n,A); 
	printf("%d\n",cnt);
	for(int i=0;i<n;i++)
		printf("%d\n",A[i]);
	return 0;
}
### Prompt

Please create a solution in Cpp to the following problem:

Shell Sort

Shell Sort is a generalization of Insertion Sort to arrange a list of $n$ elements $A$.


1  insertionSort(A, n, g)
2      for i = g to n-1
3          v = A[i]
4          j = i - g
5          while j >= 0 && A[j] > v
6              A[j+g] = A[j]
7              j = j - g
8              cnt++
9          A[j+g] = v
10
11 shellSort(A, n)
12     cnt = 0
13     m = ?
14     G[] = {?, ?,..., ?}
15     for i = 0 to m-1
16         insertionSort(A, n, G[i])


A function shellSort(A, n) performs a function insertionSort(A, n, g), which considers every $g$-th elements. Beginning with large values of $g$, it repeats the insertion sort with smaller $g$.

Your task is to complete the above program by filling ?. Write a program which reads an integer $n$ and a sequence $A$, and prints $m$, $G_i (i = 0, 1, ..., m − 1)$ in the pseudo code and the sequence $A$ in ascending order. The output of your program must meet the following requirements:

* $1 \leq m \leq 100$
* $0 \leq G_i \leq n$
* cnt does not exceed $\lceil n^{1.5}\rceil$

Constraints

* $1 \leq n \leq 1,000,000$
* $0 \leq A_i \leq 10^9$

Input

In the first line, an integer $n$ is given. In the following $n$ lines, $A_i (i=0,1,...,n-1)$ are given for each line.

Output

In the first line, print an integer $m$. In the second line, print $m$ integers $G_i (i=0,1,...,m-1)$ separated by single space character in a line.
In the third line, print cnt in a line. In the following $n$ lines, print $A_i (i=0,1,...,n-1)$ respectively.

This problem has multiple solutions and the judge will be performed by a special validator.

Examples

Input

5
5
1
4
3
2


Output

2
4 1
3
1
2
3
4
5


Input

3
3
2
1


Output

1
1
3
1
2
3

### Response

```cpp
#include<bits/stdc++.h>

using namespace std;

const int MAXN=1000010;

int cnt=0,G[100];

void Insertion_Sort(int s,int t,int n,int* A)
{
	for(int i=s+t;i<n;i+=t)
	{
		int key=A[i],j=i-t;
		while(j>=0&&A[j]>key)
		{
			A[j+t]=A[j];
			j-=t;
			cnt++;
		}
		if(A[j+t]!=key)
		{
			A[j+t]=key;
			//cnt++;
		}
	}
}

int main()
{
	for(int i=0;(G[i]=G[i-1]*3+1)<=MAXN;i++);
	static int n,A[MAXN];
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%d",&A[i]);
	int t;
	for(t=0;G[t]<=n;t++);
	printf("%d\n",t);
	for(int i=t-1;i>=0;i--)
		printf("%d%c",G[i],i==0?'\n':' ');
	for(int i=t-1;i>=0;i--)
		for(int j=0;j<G[i];j++)
			Insertion_Sort(j,G[i],n,A); 
	printf("%d\n",cnt);
	for(int i=0;i<n;i++)
		printf("%d\n",A[i]);
	return 0;
}
```