//希尔排序
#include<iostream>
using namespace std;
#define N 1000005
long long cnt = 0;
int G[102];
int A[N];
void insertionSort(int A[],int n,int g)
{
	int v,j;
	for(int i =g;i<n;i++)
	{
		v=A[i];
		j = i-g;
		while(j>=0&&A[j]>v)
		{
			A[j+g] = A[j];
			j=j - g;
			cnt++;
		}
		A[j+g] = v; 
	}
} 

void shellSort(int A[],int n)
{
	int m = n ,i=0;
	while(m/3!=0)
	{
		G[i] = m/3+1;
		m = G[i];
		i++;
	}
	G[i]=1;
	m = i+1;
	cout<<m<<endl;
	for(i =0;i<m;i++)
	{
		insertionSort(A,n,G[i]);
		if(i<m-1)
		cout<<G[i]<<' ';
		else 
		cout<<G[i]<<endl;
	}
	
}
int main()
{
	int n;
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>A[i];
	}
	shellSort(A,n);
	cout<<cnt<<endl;
	for(int i=0;i<n;i++)
	{
		cout<<A[i]<<endl;
	}
	return 0;
	
}


### Prompt

Please formulate a CPP solution 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
//希尔排序
#include<iostream>
using namespace std;
#define N 1000005
long long cnt = 0;
int G[102];
int A[N];
void insertionSort(int A[],int n,int g)
{
	int v,j;
	for(int i =g;i<n;i++)
	{
		v=A[i];
		j = i-g;
		while(j>=0&&A[j]>v)
		{
			A[j+g] = A[j];
			j=j - g;
			cnt++;
		}
		A[j+g] = v; 
	}
} 

void shellSort(int A[],int n)
{
	int m = n ,i=0;
	while(m/3!=0)
	{
		G[i] = m/3+1;
		m = G[i];
		i++;
	}
	G[i]=1;
	m = i+1;
	cout<<m<<endl;
	for(i =0;i<m;i++)
	{
		insertionSort(A,n,G[i]);
		if(i<m-1)
		cout<<G[i]<<' ';
		else 
		cout<<G[i]<<endl;
	}
	
}
int main()
{
	int n;
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>A[i];
	}
	shellSort(A,n);
	cout<<cnt<<endl;
	for(int i=0;i<n;i++)
	{
		cout<<A[i]<<endl;
	}
	return 0;
	
}


```