#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;

long long c;
int l;
int A[1000000];
int n;
vector<int> G;


void ins(int A[],int n,int g){
  for(int i=g;i<n;i++){
    int v=A[i];
    int j=i-g;
    while(j>=0 && A[j] >v){
      A[j+g]=A[j];
      j -= g;
      c++;
    }
    A[j+g]= v;
  }
}


void she(int A[],int n){
  for(int h=1; ; ){
    if(h>n) break;
    G.push_back(h);
    h= 3*h+1;
  }

  for(int i=G.size()-1;i>=0;i--){
    ins (A,n,G[i]);
  }
}


int main(){
  cin >> n;
  for(int i=0;i<n;i++) scanf("%d",&A[i]);
  c=0;

  she(A,n);

  cout << G.size() << endl;
    for(int i= G.size()-1;i>=0;i--){
      printf("%d",G[i]);
      if(i) printf(" ");
    }
    printf("\n");
    printf("%d\n",c);
    for(int i=0;i<n;i++) printf("%d\n",A[i]);

    return 0;
}


### Prompt

Create a solution in cpp for 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>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;

long long c;
int l;
int A[1000000];
int n;
vector<int> G;


void ins(int A[],int n,int g){
  for(int i=g;i<n;i++){
    int v=A[i];
    int j=i-g;
    while(j>=0 && A[j] >v){
      A[j+g]=A[j];
      j -= g;
      c++;
    }
    A[j+g]= v;
  }
}


void she(int A[],int n){
  for(int h=1; ; ){
    if(h>n) break;
    G.push_back(h);
    h= 3*h+1;
  }

  for(int i=G.size()-1;i>=0;i--){
    ins (A,n,G[i]);
  }
}


int main(){
  cin >> n;
  for(int i=0;i<n;i++) scanf("%d",&A[i]);
  c=0;

  she(A,n);

  cout << G.size() << endl;
    for(int i= G.size()-1;i>=0;i--){
      printf("%d",G[i]);
      if(i) printf(" ");
    }
    printf("\n");
    printf("%d\n",c);
    for(int i=0;i<n;i++) printf("%d\n",A[i]);

    return 0;
}


```