#include <iostream>
#include <vector>
using namespace std;

void solve(){
  int n; cin >> n;
  vector<int> a(n), g;
  for(int i = 0; i < n; i++){
    cin >> a[i];
  }
  g.push_back(1);
  while(g[g.size() - 1] < n){
    g.push_back(g[g.size() - 1] * 3 + 1);
  }
  if(g.size() > 1) g.pop_back();
  int m = g.size();
  long long cnt = 0;
  for(int i = m - 1; i >= 0; i--){
    int x = g[i];
    for(int i = x; i < n; i++){
      int y = a[i];
      int j;
      for(j = i - x; j >= 0 && a[j] > y; j -= x){
        a[j + x] = a[j];
        cnt++;
      }
      a[j + x] = y;
    }
  }
  cout << m << endl;
  for(int i = m - 1; i >= 1; i--) cout << g[i] << " "; cout << g[0] << endl;
  cout << cnt << endl;
  for(int i = 0; i < n; i++) cout << a[i] << endl;
  return;
}

int main(){
  solve();
  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 <vector>
using namespace std;

void solve(){
  int n; cin >> n;
  vector<int> a(n), g;
  for(int i = 0; i < n; i++){
    cin >> a[i];
  }
  g.push_back(1);
  while(g[g.size() - 1] < n){
    g.push_back(g[g.size() - 1] * 3 + 1);
  }
  if(g.size() > 1) g.pop_back();
  int m = g.size();
  long long cnt = 0;
  for(int i = m - 1; i >= 0; i--){
    int x = g[i];
    for(int i = x; i < n; i++){
      int y = a[i];
      int j;
      for(j = i - x; j >= 0 && a[j] > y; j -= x){
        a[j + x] = a[j];
        cnt++;
      }
      a[j + x] = y;
    }
  }
  cout << m << endl;
  for(int i = m - 1; i >= 1; i--) cout << g[i] << " "; cout << g[0] << endl;
  cout << cnt << endl;
  for(int i = 0; i < n; i++) cout << a[i] << endl;
  return;
}

int main(){
  solve();
  return 0;
}


```