#include<bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); i++)
using namespace std;

int64_t cnt = 0;
vector<int> G;

void insertionsort(vector<int> &A,int n,int g){
  for(int i = g; i < n; i++){
    int v = A.at(i);
    int j = i - g;
    while(j >= 0 && A.at(j) > v){
      A.at(j+g) = A.at(j);
      j -= g;
      cnt++;
    }
    A.at(j+g) = v;
  }
}

void shellsort(vector<int> &A,int n){
  int m = G.size();
  rep(i,m) insertionsort(A,n,G.at(m-1-i));
}

int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  rep(i,N) cin >> A.at(i);
  int h = 1;
  while(h <= N){
    G.push_back(h);
    h = (3 * h) + 1;
  }
  int m  = G.size();
  cout << m << endl;

  shellsort(A,N);
  for(int i = m - 1; i >= 0; i--){
    cout << G.at(i);
    if(i) cout << " ";
  }
  cout << "\n" << cnt << endl;
  rep(i,N) cout << A.at(i) << endl;
}


### Prompt

Please formulate 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>
#define rep(i,n) for(int i = 0; i < (n); i++)
using namespace std;

int64_t cnt = 0;
vector<int> G;

void insertionsort(vector<int> &A,int n,int g){
  for(int i = g; i < n; i++){
    int v = A.at(i);
    int j = i - g;
    while(j >= 0 && A.at(j) > v){
      A.at(j+g) = A.at(j);
      j -= g;
      cnt++;
    }
    A.at(j+g) = v;
  }
}

void shellsort(vector<int> &A,int n){
  int m = G.size();
  rep(i,m) insertionsort(A,n,G.at(m-1-i));
}

int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  rep(i,N) cin >> A.at(i);
  int h = 1;
  while(h <= N){
    G.push_back(h);
    h = (3 * h) + 1;
  }
  int m  = G.size();
  cout << m << endl;

  shellsort(A,N);
  for(int i = m - 1; i >= 0; i--){
    cout << G.at(i);
    if(i) cout << " ";
  }
  cout << "\n" << cnt << endl;
  rep(i,N) cout << A.at(i) << endl;
}


```