#include<iostream>
using namespace std;


 int InsertionSort(int* a, int n, int g)
{
	int tmp, j, count = 0;
	for (int i = g; i < n; i++)
	{
		tmp = a[i];
		for (j = i - g; j >= 0 && a[j] > tmp; j -= g)
		{
			a[j + g] = a[j];
			count++;
		}
		a[j + g] = tmp;
	}
	return count;
}

int ShellSort(int* a, int n)
{
	int m, g[100],count = 0;
	for (m = 1; m * m * m <= n; m++)
		continue;
	m--;
	cout << m << endl;
	for (int i = 0; i < m; i++)
	{
	    g[i] = (m - i) * (m - i);
		if (i)
			cout << " ";
		cout << g[i];
	}
	for (int i = 0; i < m; i++)
		count += InsertionSort(a, n, g[i]);

	return count;
}

int main()
{
	int n, a[1000000], count;
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> a[i];
	count = ShellSort(a, n);
	cout << endl << count << endl;
	for (int i = 0; i < n; i++)
		cout << a[i] << endl;

	return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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>
using namespace std;


 int InsertionSort(int* a, int n, int g)
{
	int tmp, j, count = 0;
	for (int i = g; i < n; i++)
	{
		tmp = a[i];
		for (j = i - g; j >= 0 && a[j] > tmp; j -= g)
		{
			a[j + g] = a[j];
			count++;
		}
		a[j + g] = tmp;
	}
	return count;
}

int ShellSort(int* a, int n)
{
	int m, g[100],count = 0;
	for (m = 1; m * m * m <= n; m++)
		continue;
	m--;
	cout << m << endl;
	for (int i = 0; i < m; i++)
	{
	    g[i] = (m - i) * (m - i);
		if (i)
			cout << " ";
		cout << g[i];
	}
	for (int i = 0; i < m; i++)
		count += InsertionSort(a, n, g[i]);

	return count;
}

int main()
{
	int n, a[1000000], count;
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> a[i];
	count = ShellSort(a, n);
	cout << endl << count << endl;
	for (int i = 0; i < n; i++)
		cout << a[i] << endl;

	return 0;
}

```