#include<stdio.h>
#include<math.h>

#define N 1000000

int main(){
  int inser[N];
  int i,j,g,value;
  int num,cnt;
  int m;
  int shell[N];
  int k;

  scanf("%d",&num);
  for(i=0;i<num;i++) scanf("%d",&inser[i]);

  //shellsort
  cnt = 0;

  j=0;

  for(i=num/2;i>0;i=i/2){
    shell[j] = i;
    j++;
  }
  m=j+1;
    
  for(k=0;k<=m-1;k++){
    //insertionsort
    for(i=shell[k];i<=num-1;i++){
      value = inser[i];
      j = i - shell[k];
      while(j>=0 && inser[j] > value){
	inser[j+shell[k]] = inser[j];
	j = j - shell[k];
	cnt++;
	inser[j+shell[k]] = value;
      }
    }
  }

  printf("%d\n",m);
  for(i=0;i<m;i++){
    if(i) printf(" ");
    printf("%d",shell[i]);
  }
  printf("\n");

  printf("%d\n",cnt);

  for(i=0;i<num;i++){
    printf("%d\n",inser[i]);
  }
    
  return 0;
}




### Prompt

Generate 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<stdio.h>
#include<math.h>

#define N 1000000

int main(){
  int inser[N];
  int i,j,g,value;
  int num,cnt;
  int m;
  int shell[N];
  int k;

  scanf("%d",&num);
  for(i=0;i<num;i++) scanf("%d",&inser[i]);

  //shellsort
  cnt = 0;

  j=0;

  for(i=num/2;i>0;i=i/2){
    shell[j] = i;
    j++;
  }
  m=j+1;
    
  for(k=0;k<=m-1;k++){
    //insertionsort
    for(i=shell[k];i<=num-1;i++){
      value = inser[i];
      j = i - shell[k];
      while(j>=0 && inser[j] > value){
	inser[j+shell[k]] = inser[j];
	j = j - shell[k];
	cnt++;
	inser[j+shell[k]] = value;
      }
    }
  }

  printf("%d\n",m);
  for(i=0;i<m;i++){
    if(i) printf(" ");
    printf("%d",shell[i]);
  }
  printf("\n");

  printf("%d\n",cnt);

  for(i=0;i<num;i++){
    printf("%d\n",inser[i]);
  }
    
  return 0;
}




```