#include <bits/stdc++.h>
using namespace std;

#define rep(i, u) for (int i = 0; i < u; i++)

using ll = long long;
using ull = unsigned long long;

int main() {
  int n;
  int a[1000000] = {};
  cin >> n;
  rep(i, n) cin >> a[i];
  int cnt = 0;
  int m = 0;
  int g[1000000] = {};
  for (int i = 1; ; i = 3 * i + 1) {
    g[m] = i;
    if (g[m] > n) break;
    m++;
  }
  reverse(g, g + m);
  rep(i, m) {
    for (int j = g[i]; j < n; j++) {
      int v = a[j];
      int k = j - g[i];
      while (k >= 0 && a[k] > v) {
        a[k + g[i]] = a[k];
        k -= g[i];
        cnt++;
      }
      a[k + g[i]] = v;
    }
  }
  cout << m << endl;
  rep(i, m) {
    cout << g[i];
    if (i != m - 1) cout << ' ';
    else cout << endl;
  }
  cout << cnt << endl;
  rep(i, n) cout << a[i] << endl;

  return 0;
}


### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
using namespace std;

#define rep(i, u) for (int i = 0; i < u; i++)

using ll = long long;
using ull = unsigned long long;

int main() {
  int n;
  int a[1000000] = {};
  cin >> n;
  rep(i, n) cin >> a[i];
  int cnt = 0;
  int m = 0;
  int g[1000000] = {};
  for (int i = 1; ; i = 3 * i + 1) {
    g[m] = i;
    if (g[m] > n) break;
    m++;
  }
  reverse(g, g + m);
  rep(i, m) {
    for (int j = g[i]; j < n; j++) {
      int v = a[j];
      int k = j - g[i];
      while (k >= 0 && a[k] > v) {
        a[k + g[i]] = a[k];
        k -= g[i];
        cnt++;
      }
      a[k + g[i]] = v;
    }
  }
  cout << m << endl;
  rep(i, m) {
    cout << g[i];
    if (i != m - 1) cout << ' ';
    else cout << endl;
  }
  cout << cnt << endl;
  rep(i, n) cout << a[i] << endl;

  return 0;
}


```