#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int num;
vector<int> line;
int cnt;
void shellsort(int d){
	for(int i=0;i<d;++i){
		for(int j=i;j<line.size();j+=d){
			int place = j;
			while(place - d >= 0 && line[place - d] > line[place]){
				swap(line[place - d],line[place]);
				++cnt;
				place-=d;
			}
		}
	}
}
int main(){
	cin>>num;
	line.resize(num); 
	for(int i=0;i<num;++i){
		cin>>line[i];
	}
	vector<int> d;
	d.push_back(1);
	while(d.back() <= num){
		d.push_back(d.back()*4+1);
	}
	d.pop_back();
	cout<<d.size()<<endl;
	for(int i=d.size()-1;i>=0;--i){
		if(i!=d.size()-1){
			cout<<" ";
		}
		cout<<d[i];
		shellsort(d[i]);
	}
	cout<<endl;
	cout<<cnt<<endl;
	for(int i=0;i<line.size();++i){
		cout<<line[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>
#include<algorithm>
using namespace std;
int num;
vector<int> line;
int cnt;
void shellsort(int d){
	for(int i=0;i<d;++i){
		for(int j=i;j<line.size();j+=d){
			int place = j;
			while(place - d >= 0 && line[place - d] > line[place]){
				swap(line[place - d],line[place]);
				++cnt;
				place-=d;
			}
		}
	}
}
int main(){
	cin>>num;
	line.resize(num); 
	for(int i=0;i<num;++i){
		cin>>line[i];
	}
	vector<int> d;
	d.push_back(1);
	while(d.back() <= num){
		d.push_back(d.back()*4+1);
	}
	d.pop_back();
	cout<<d.size()<<endl;
	for(int i=d.size()-1;i>=0;--i){
		if(i!=d.size()-1){
			cout<<" ";
		}
		cout<<d[i];
		shellsort(d[i]);
	}
	cout<<endl;
	cout<<cnt<<endl;
	for(int i=0;i<line.size();++i){
		cout<<line[i]<<endl;
	}
	return 0;
}

```