#include<stdio.h>

int cnt;
void InsertionSort(int* a, int n, int g){
	int i,j,key;
	for(i=1;i<n;i++){
		key=a[i];
		j=i-g;
		while(j>=0 && a[j]>key){
			a[j+g]=a[j];
			j-=g;
			cnt++;
		}
		a[j+g]=key;
	}
}

void ShellSort(int* a, int n){
	int i;	int m=1;
	int G[100];
	G[1]=n;
	while(1){
		++m;
		G[m]=G[m-1]/3;
		//printf("G[%d]=%d\n",m,G[m]);
		if(G[m]<=1){
			//printf("ERROR: G[%d]=%d\n",m,G[m]);
			G[m]=1;
			break;
		}
	}
		printf("%d\n",m);

	for(i=1;i<=m;i++){
		if(i>1)printf(" ");
		printf("%d",G[i]);
	}printf("\n");
	cnt=0;
	for(i=1;i<=m;i++){
		if(G[i]<=n)InsertionSort(a,n,G[i]);
	}
	printf("%d\n",cnt);
}

int main(){
	int i,n;	scanf("%d",&n);
	int array[1000000];
	for(i=0;i<n;i++)scanf("%d",&array[i]);
	ShellSort(array, n);

	for(i=0;i<n;i++){
		printf("%d\n",array[i]);
	}


	return 0;
}


### Prompt

Develop a solution in cpp to the problem described below:

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<stdio.h>

int cnt;
void InsertionSort(int* a, int n, int g){
	int i,j,key;
	for(i=1;i<n;i++){
		key=a[i];
		j=i-g;
		while(j>=0 && a[j]>key){
			a[j+g]=a[j];
			j-=g;
			cnt++;
		}
		a[j+g]=key;
	}
}

void ShellSort(int* a, int n){
	int i;	int m=1;
	int G[100];
	G[1]=n;
	while(1){
		++m;
		G[m]=G[m-1]/3;
		//printf("G[%d]=%d\n",m,G[m]);
		if(G[m]<=1){
			//printf("ERROR: G[%d]=%d\n",m,G[m]);
			G[m]=1;
			break;
		}
	}
		printf("%d\n",m);

	for(i=1;i<=m;i++){
		if(i>1)printf(" ");
		printf("%d",G[i]);
	}printf("\n");
	cnt=0;
	for(i=1;i<=m;i++){
		if(G[i]<=n)InsertionSort(a,n,G[i]);
	}
	printf("%d\n",cnt);
}

int main(){
	int i,n;	scanf("%d",&n);
	int array[1000000];
	for(i=0;i<n;i++)scanf("%d",&array[i]);
	ShellSort(array, n);

	for(i=0;i<n;i++){
		printf("%d\n",array[i]);
	}


	return 0;
}


```