#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>

using namespace std;

int main(void)
{
  long long cnt = 0;
  int interval = 1, n, i = 0;
  int num[1000000] = {0};
  int G[13] = {0};

  cin >> n;

  while(interval <= n){
    G[i] = interval;
    interval = interval * 3 + 1;
    i++;
  }

  int Gstart = i;

  for(i = 0;i < n;i++){
    cin >> num[i];
  }

  for(int k = Gstart - 1;k >= 0;k--){
    for(int i = G[k];i < n;i++){
      int v = num[i];
      int j = i - G[k];
      while(j >= 0 && num[j] > v){
	num[j + G[k]] = num[j];
	j -= G[k];
	cnt++;
      }
      num[j + G[k]] = v;
    }
  }

  cout << Gstart << endl;

  for(i = Gstart - 1;i >= 0;i--){
    cout << G[i] << ' ';
  }

  cout << endl << cnt << endl;

  for(i = 0;i < n;i++){
    cout << num[i] << endl;
  }
  
  return 0;
}


### Prompt

Your challenge is to write 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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>

using namespace std;

int main(void)
{
  long long cnt = 0;
  int interval = 1, n, i = 0;
  int num[1000000] = {0};
  int G[13] = {0};

  cin >> n;

  while(interval <= n){
    G[i] = interval;
    interval = interval * 3 + 1;
    i++;
  }

  int Gstart = i;

  for(i = 0;i < n;i++){
    cin >> num[i];
  }

  for(int k = Gstart - 1;k >= 0;k--){
    for(int i = G[k];i < n;i++){
      int v = num[i];
      int j = i - G[k];
      while(j >= 0 && num[j] > v){
	num[j + G[k]] = num[j];
	j -= G[k];
	cnt++;
      }
      num[j + G[k]] = v;
    }
  }

  cout << Gstart << endl;

  for(i = Gstart - 1;i >= 0;i--){
    cout << G[i] << ' ';
  }

  cout << endl << cnt << endl;

  for(i = 0;i < n;i++){
    cout << num[i] << endl;
  }
  
  return 0;
}


```