#include <bits/stdc++.h>
#include <iostream>
using namespace std;
int main(){
  int N;
  cin >> N;
  int A[N];
  for(int i=0;i<N;i++){
    cin >> A[i];
  }
  int m=0;
  int sum=0;
  int G[13]={1,4,13,40,121,364,1093,3280,9841,29524,88573,265720,797161};
  for(int i=12;i>=0;i--){
    if(N/G[i]>=1){
      m=i;
      break;
    }
  }
  cout << m+1 << endl;
  for(int i=m;i>=0;i--){
    for(int j=G[i];j<=N-1;j++){
    int v=A[j];
    int k=j-G[i];
 while(k>=0 && A[k]>v){
    A[k+G[i]]=A[k];
    k=k-G[i];
    sum++;
    A[k+G[i]]=v;
  }
  }
  if(i>0){
    cout << G[i] << " ";
  }
  else if(i==0){
    cout << G[i] << endl << sum << endl;
  }
 }
 for(int i=0;i<N;i++){
    cout << A[i] << endl;
  }
}  

### Prompt

Your task is to create a CPP solution 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>
#include <iostream>
using namespace std;
int main(){
  int N;
  cin >> N;
  int A[N];
  for(int i=0;i<N;i++){
    cin >> A[i];
  }
  int m=0;
  int sum=0;
  int G[13]={1,4,13,40,121,364,1093,3280,9841,29524,88573,265720,797161};
  for(int i=12;i>=0;i--){
    if(N/G[i]>=1){
      m=i;
      break;
    }
  }
  cout << m+1 << endl;
  for(int i=m;i>=0;i--){
    for(int j=G[i];j<=N-1;j++){
    int v=A[j];
    int k=j-G[i];
 while(k>=0 && A[k]>v){
    A[k+G[i]]=A[k];
    k=k-G[i];
    sum++;
    A[k+G[i]]=v;
  }
  }
  if(i>0){
    cout << G[i] << " ";
  }
  else if(i==0){
    cout << G[i] << endl << sum << endl;
  }
 }
 for(int i=0;i<N;i++){
    cout << A[i] << endl;
  }
}  

```