#include<bits/stdc++.h>
using namespace std;
int cnt  = 0;
int shell(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;
		}
	}
	return 0;
}
int main(){
	int n,m = 0;
	cin>>n;
	int A[n];
	int g[13] = {1,4,13,40,121,364,1093,3280,9841,29524,88573,265720,797161};
	for(int  i = 12;i>=0;i--){
		if(n/g[i] >=1){
			m = i;
			break;

		}
		
	}
	for(int i = 0;i<n;i++){
		cin>>A[i];
	}
	
	for(int i = 0;i<=m;i++){
		shell(A,n,g[m-i]);
	}
	cout<<m+1<<endl;
	for(int i = m;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

Create a solution in cpp for 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;
int cnt  = 0;
int shell(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;
		}
	}
	return 0;
}
int main(){
	int n,m = 0;
	cin>>n;
	int A[n];
	int g[13] = {1,4,13,40,121,364,1093,3280,9841,29524,88573,265720,797161};
	for(int  i = 12;i>=0;i--){
		if(n/g[i] >=1){
			m = i;
			break;

		}
		
	}
	for(int i = 0;i<n;i++){
		cin>>A[i];
	}
	
	for(int i = 0;i<=m;i++){
		shell(A,n,g[m-i]);
	}
	cout<<m+1<<endl;
	for(int i = m;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;
}

```