#include <iostream>
#include <cstring>
using namespace std;
int n,a[1000000];
int g[100];
int cnt=0;

void shellsort(int j){
    int h=g[j];
    int i;
    for(i=h;i<n;i++){
        int v=a[i];
        int k=i-h;
        while(k>=0&&a[k]>v){
            a[k+h]=a[k];
            cnt=cnt+1;
            k-=h;
        }
        a[k+h]=v;
    }
}

int main()
{
    cin>>n;
    int i,j,k;
    for(i=0;i<n;i++){
        cin>>a[i];
    }
    memset(g,0,sizeof(g));
    i=0;
    g[i]=1;
    //??????????????????
    if(n==1)i=1;
    else
        while(g[i]<n){g[i+1]=g[i++]*3+1;}
    cout<<i<<endl;
    for(j=i-1;j>=0;j--){
        cout<<g[j];
        if(j!=0)cout<<" ";
    }
    cout<<endl;
    for(j=i-1;j>=0;j--){
        shellsort(j);
    }
    cout<<cnt<<endl;
    for(k=0;k<n;k++){
        cout<<a[k]<<endl;
    }
    return 0;
}
### 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 <cstring>
using namespace std;
int n,a[1000000];
int g[100];
int cnt=0;

void shellsort(int j){
    int h=g[j];
    int i;
    for(i=h;i<n;i++){
        int v=a[i];
        int k=i-h;
        while(k>=0&&a[k]>v){
            a[k+h]=a[k];
            cnt=cnt+1;
            k-=h;
        }
        a[k+h]=v;
    }
}

int main()
{
    cin>>n;
    int i,j,k;
    for(i=0;i<n;i++){
        cin>>a[i];
    }
    memset(g,0,sizeof(g));
    i=0;
    g[i]=1;
    //??????????????????
    if(n==1)i=1;
    else
        while(g[i]<n){g[i+1]=g[i++]*3+1;}
    cout<<i<<endl;
    for(j=i-1;j>=0;j--){
        cout<<g[j];
        if(j!=0)cout<<" ";
    }
    cout<<endl;
    for(j=i-1;j>=0;j--){
        shellsort(j);
    }
    cout<<cnt<<endl;
    for(k=0;k<n;k++){
        cout<<a[k]<<endl;
    }
    return 0;
}
```