#include <iostream>
#include <math.h>
using namespace std;

int insSort(int *a, int n, int g) {
	int j, key, cnt = 0;
	for (int i = g; i < n; i++) {
		key = a[i];
		j = i - g;
		while(( j >= 0) && (a[j] > key)) {
			a[j+g] = a[j];
			j = j - g;
			cnt++;
		}
		a[j+g] = key;
	}
	return cnt;
}

int main(){
	int n, m, cnt=0;
	cin >> n;
	int *a = new int[n];
	for (int i = 0; i < n; i++)
		cin >> a[i];
	for (m = 1; m < n + 2; m++) {
		if ((pow( 3 , m ) -1) / 2 > n) {
			m = m - 1;
			break;
		}
	}
	int *g = new int[m];
	for (int i = 0; i < m; i++ ) {
		g[i] = (pow(3, m - i) -1) / 2;
		cnt += insSort(a, n, g[i]);
	}
	cout << m << endl;
	for (int i = 0; i < m - 1; i++ )
		cout << g[i] << ' ';
	cout << g[m - 1] << endl;
	cout << cnt << endl;
	for (int i = 0; i < n; i++)
		cout << a[i] << endl;
	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 <math.h>
using namespace std;

int insSort(int *a, int n, int g) {
	int j, key, cnt = 0;
	for (int i = g; i < n; i++) {
		key = a[i];
		j = i - g;
		while(( j >= 0) && (a[j] > key)) {
			a[j+g] = a[j];
			j = j - g;
			cnt++;
		}
		a[j+g] = key;
	}
	return cnt;
}

int main(){
	int n, m, cnt=0;
	cin >> n;
	int *a = new int[n];
	for (int i = 0; i < n; i++)
		cin >> a[i];
	for (m = 1; m < n + 2; m++) {
		if ((pow( 3 , m ) -1) / 2 > n) {
			m = m - 1;
			break;
		}
	}
	int *g = new int[m];
	for (int i = 0; i < m; i++ ) {
		g[i] = (pow(3, m - i) -1) / 2;
		cnt += insSort(a, n, g[i]);
	}
	cout << m << endl;
	for (int i = 0; i < m - 1; i++ )
		cout << g[i] << ' ';
	cout << g[m - 1] << endl;
	cout << cnt << endl;
	for (int i = 0; i < n; i++)
		cout << a[i] << endl;
	return 0;
}
```