#include<iostream>
using namespace std;
int main(){
    int n,cnt=0,m=0;
    cin>>n;
    int a[n];
    int g[100]={1};
    for (int i=0;i<n;i++){
        cin>>a[i];
    }
    while(g[m]<n){
        g[m+1]+=3*g[m];
        m++;
    }
    if(n==1){
        m=1;
    }
    for(int i=m-1;i>=0;i--){
        for(int k=g[i];k<n;k++){
            int v=a[k];
            int j=k-g[i];
            while(j>=0&&a[j]>v){
                a[j+g[i]]=a[j];
                j=j-g[i];
                cnt++;
            }
            a[j+g[i]]=v;
        }
    }
    cout<<m<<endl;
    for(int i=m-1;i>0;i--){
        cout<<g[i]<<" ";
    }
    cout<<g[0]<<endl;
    cout<<cnt<<endl;
    for(int i=0;i<n;i++){
        cout<<a[i]<<endl;
    }
    return 0;
}

### Prompt

In cpp, your task is to solve 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>
using namespace std;
int main(){
    int n,cnt=0,m=0;
    cin>>n;
    int a[n];
    int g[100]={1};
    for (int i=0;i<n;i++){
        cin>>a[i];
    }
    while(g[m]<n){
        g[m+1]+=3*g[m];
        m++;
    }
    if(n==1){
        m=1;
    }
    for(int i=m-1;i>=0;i--){
        for(int k=g[i];k<n;k++){
            int v=a[k];
            int j=k-g[i];
            while(j>=0&&a[j]>v){
                a[j+g[i]]=a[j];
                j=j-g[i];
                cnt++;
            }
            a[j+g[i]]=v;
        }
    }
    cout<<m<<endl;
    for(int i=m-1;i>0;i--){
        cout<<g[i]<<" ";
    }
    cout<<g[0]<<endl;
    cout<<cnt<<endl;
    for(int i=0;i<n;i++){
        cout<<a[i]<<endl;
    }
    return 0;
}

```