#include<iostream>
#include<vector>

using namespace std;

long long cnt;
int i,A[1000000],n;
vector<int> G;


void insertionSort(int A[],int n,int g){
	for(int i=g;i<n;i++){
		int v = A[i];
		int j = i - g;
		while(j >= 0 && A[j] > v){
			A[j+g] = A[j];
			j -= g;
			cnt++;
		}
		A[j+g] = v;
	}
}


void shellSort(int A[],int n){
	for(int h=1;h <= n;h = 3*h+1)
		G.push_back(h);
	for(int i=G.size() -1;i>=0;i--)
		insertionSort(A,n,G[i]);
}

int main(){
	cin >> n;
	for(int i=0;i<n;i++)
		cin >> A[i];
	cnt = 0;
	
	shellSort(A,n);
	
	cout <<G.size() << endl;
	for(int i= G.size() -1;i>0;i--)
		cout << G[i] << ' ';
	cout << G[0] << endl;
	cout << cnt << endl;
	for(int i=0;i<n;i++)
		cout << A[i] << endl;
	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<iostream>
#include<vector>

using namespace std;

long long cnt;
int i,A[1000000],n;
vector<int> G;


void insertionSort(int A[],int n,int g){
	for(int i=g;i<n;i++){
		int v = A[i];
		int j = i - g;
		while(j >= 0 && A[j] > v){
			A[j+g] = A[j];
			j -= g;
			cnt++;
		}
		A[j+g] = v;
	}
}


void shellSort(int A[],int n){
	for(int h=1;h <= n;h = 3*h+1)
		G.push_back(h);
	for(int i=G.size() -1;i>=0;i--)
		insertionSort(A,n,G[i]);
}

int main(){
	cin >> n;
	for(int i=0;i<n;i++)
		cin >> A[i];
	cnt = 0;
	
	shellSort(A,n);
	
	cout <<G.size() << endl;
	for(int i= G.size() -1;i>0;i--)
		cout << G[i] << ' ';
	cout << G[0] << endl;
	cout << cnt << endl;
	for(int i=0;i<n;i++)
		cout << A[i] << endl;
	return 0;

}
		
```