#include<bits/stdc++.h>
using namespace std;
const int MAX_NUM = 1000000+7;
int a[MAX_NUM];
int g[107];
int m; 
int n;
int cnt;
void insertSort(int g){
	int i;
	for(i = g; i < n; i++){
		int key = a[i];
		int j;
		for(j = i-g; j>=0 && a[j] > key;j-=g){
			a[j+g] = a[j];
			cnt++; 
		}
		a[j+g] = key;
	}
}
void shellSort(){
	cnt = 0;
	m = 0;
	int k = 1;
	while(true){
		if(k > n) break;
		g[m++] = k;
		k= 3*k+1;
	}
	
	cout << m << endl;
	
	int q;
	for(q = m-1; q>=0 ;q--){
		if(q!=m-1) cout << " ";
		cout << g[q]; 
	}
	cout << endl;
	int i;
	for(i = m-1; i >=0 ; i--){
		insertSort(g[i]);
	}
}
int main(){
	
	
	cin >> n;
	int i;
	for(i = 0; i < n; i++){
		cin >> a[i];
	}
	
	shellSort();
	cout << cnt<< endl;
	for(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<bits/stdc++.h>
using namespace std;
const int MAX_NUM = 1000000+7;
int a[MAX_NUM];
int g[107];
int m; 
int n;
int cnt;
void insertSort(int g){
	int i;
	for(i = g; i < n; i++){
		int key = a[i];
		int j;
		for(j = i-g; j>=0 && a[j] > key;j-=g){
			a[j+g] = a[j];
			cnt++; 
		}
		a[j+g] = key;
	}
}
void shellSort(){
	cnt = 0;
	m = 0;
	int k = 1;
	while(true){
		if(k > n) break;
		g[m++] = k;
		k= 3*k+1;
	}
	
	cout << m << endl;
	
	int q;
	for(q = m-1; q>=0 ;q--){
		if(q!=m-1) cout << " ";
		cout << g[q]; 
	}
	cout << endl;
	int i;
	for(i = m-1; i >=0 ; i--){
		insertSort(g[i]);
	}
}
int main(){
	
	
	cin >> n;
	int i;
	for(i = 0; i < n; i++){
		cin >> a[i];
	}
	
	shellSort();
	cout << cnt<< endl;
	for(i = 0; i < n; i++){
		cout << a[i] << endl;
	}
	
	return 0;
}

```