# include <iostream>
# include <deque>
using namespace std; 
int n,*a;
deque<int> d; 
int cnt = 0;
void shell_sort()
{
	int y,h,k;
	for(int i = 0;i < d.size();i++)
	{
		h = d[i];
		for(int j = h;j < n;j++)
		{
			y = a[j];
			for(k = j-h; k >= 0 && y <a[k]; k -= h) 
			{
				cnt++;
				a[k+h] = a[k];
			}
			a[k+h] = y;
		}
	} 
}

int main(void)
{
	d.push_back(1);
	scanf("%d",&n);
	a = new int [n];
	for(int i = 2;i < n;i++)
	{
		if(d.size() == 100 || 3*d[0]+1 >= n) break;
		d.push_front(3*d[0]+1);
	}
	for(int i = 0;i < n;i++) scanf("%d",&a[i]);
	shell_sort();
	printf("%d\n",d.size());
	for(int i = 0;i < d.size();i++) printf("%d%c",d[i],i == d.size()-1?'\n':' ');
	printf("%d\n",cnt);
	for(int i = 0;i < n;i++) printf("%d\n",a[i]);
	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
# include <iostream>
# include <deque>
using namespace std; 
int n,*a;
deque<int> d; 
int cnt = 0;
void shell_sort()
{
	int y,h,k;
	for(int i = 0;i < d.size();i++)
	{
		h = d[i];
		for(int j = h;j < n;j++)
		{
			y = a[j];
			for(k = j-h; k >= 0 && y <a[k]; k -= h) 
			{
				cnt++;
				a[k+h] = a[k];
			}
			a[k+h] = y;
		}
	} 
}

int main(void)
{
	d.push_back(1);
	scanf("%d",&n);
	a = new int [n];
	for(int i = 2;i < n;i++)
	{
		if(d.size() == 100 || 3*d[0]+1 >= n) break;
		d.push_front(3*d[0]+1);
	}
	for(int i = 0;i < n;i++) scanf("%d",&a[i]);
	shell_sort();
	printf("%d\n",d.size());
	for(int i = 0;i < d.size();i++) printf("%d%c",d[i],i == d.size()-1?'\n':' ');
	printf("%d\n",cnt);
	for(int i = 0;i < n;i++) printf("%d\n",a[i]);
	return 0;
}



```