#include <bits/stdc++.h>
#define lp(n) for(int i = 0; i < n; i++)
#define LP(i, a, n) for(int i = a; i < n; i++)
#define lpp(i, n) for(int i = 0; i < n; i++)
using namespace std;
int cnt;
void is(int A[], int n, int g) {
  LP(i, g, n) {
    int v = A[i];
    int j = i - g;
    while (j >= 0 && A[j] > v) {
      A[j+g] = A[j];
      j = j - g;
      cnt++;
    }
    A[j+g] = v;
  }
}
int main() {
  int m = 10;
  int d = 0;
  int G[] = {29524, 9841, 3280, 1093, 364, 121, 40, 13, 4, 1};
  int n;
  cin >> n;
  for(; G[d] > n; d++);
  
  int A[1000000];
  lp(n)
    cin >> A[i];
  lp(m-d) is(A, n, G[i+d]);
  cout << m-d << endl;
  lp(m-d) cout << G[i+d] << ((i == m-d-1)? "\n" : " ");
  cout << cnt << endl;
  lp(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>
#define lp(n) for(int i = 0; i < n; i++)
#define LP(i, a, n) for(int i = a; i < n; i++)
#define lpp(i, n) for(int i = 0; i < n; i++)
using namespace std;
int cnt;
void is(int A[], int n, int g) {
  LP(i, g, n) {
    int v = A[i];
    int j = i - g;
    while (j >= 0 && A[j] > v) {
      A[j+g] = A[j];
      j = j - g;
      cnt++;
    }
    A[j+g] = v;
  }
}
int main() {
  int m = 10;
  int d = 0;
  int G[] = {29524, 9841, 3280, 1093, 364, 121, 40, 13, 4, 1};
  int n;
  cin >> n;
  for(; G[d] > n; d++);
  
  int A[1000000];
  lp(n)
    cin >> A[i];
  lp(m-d) is(A, n, G[i+d]);
  cout << m-d << endl;
  lp(m-d) cout << G[i+d] << ((i == m-d-1)? "\n" : " ");
  cout << cnt << endl;
  lp(n) cout << A[i] << endl;
  return 0;
}


```