#include<iostream>
#include<algorithm>
#include<vector>
using namespace std ;
using vi = vector<int> ;

int cnt = 0 ;

void insertionsort(vi &a,int g){
	for(int i=g;i<a.size();i++){
		int v = a.at(i) ;
		int j = i-g ;
		while(j>=0&&a.at(j)>v){
			a.at(j+g) = a.at(j) ;
			j -= g ;
			cnt++ ;
		}
		a.at(j+g) = v ;
	}
}

void shellsort(vi &g,vi &a){
	for(int i=0;i<g.size();i++) insertionsort(a,g.at(i)) ;
}

int main(){
	int n ; cin >> n ;
	vi a(n) ;
	for(int i=0;i<n;i++) cin >> a.at(i) ;
	vi g ;
	int i = 1 ;
	while(i<=n){
		g.push_back(i) ;
		i = i*3+1 ;
	}
	reverse(g.begin(),g.end()) ;
	cout << g.size() << endl ;
	for(int i=0;i<g.size();i++){
		cout << g.at(i) ;
		if(i==g.size()-1) cout << endl ;
		else cout << " " ;
	}
	shellsort(g,a) ;
	cout << cnt << endl ;
	for(int i=0;i<n;i++){
		cout << a.at(i) << endl ;
	}
}

### Prompt

Construct a CPP code solution to the problem outlined:

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<algorithm>
#include<vector>
using namespace std ;
using vi = vector<int> ;

int cnt = 0 ;

void insertionsort(vi &a,int g){
	for(int i=g;i<a.size();i++){
		int v = a.at(i) ;
		int j = i-g ;
		while(j>=0&&a.at(j)>v){
			a.at(j+g) = a.at(j) ;
			j -= g ;
			cnt++ ;
		}
		a.at(j+g) = v ;
	}
}

void shellsort(vi &g,vi &a){
	for(int i=0;i<g.size();i++) insertionsort(a,g.at(i)) ;
}

int main(){
	int n ; cin >> n ;
	vi a(n) ;
	for(int i=0;i<n;i++) cin >> a.at(i) ;
	vi g ;
	int i = 1 ;
	while(i<=n){
		g.push_back(i) ;
		i = i*3+1 ;
	}
	reverse(g.begin(),g.end()) ;
	cout << g.size() << endl ;
	for(int i=0;i<g.size();i++){
		cout << g.at(i) ;
		if(i==g.size()-1) cout << endl ;
		else cout << " " ;
	}
	shellsort(g,a) ;
	cout << cnt << endl ;
	for(int i=0;i<n;i++){
		cout << a.at(i) << endl ;
	}
}

```