#include <cstdio>
using namespace std;
const int MAXN=1e6+7;
int n,cnt=0;
int a[MAXN],g[105],h[105];
void is (int g) {
	for (int i=g;i<n;i++) {
		int v=a[i],j=i-g;
		while (j>=0&&a[j]>v) {
			a[j+g]=a[j];
			j-=g;
			cnt++;
		}
		a[j+g]=v;
	}
}
int main () {
	scanf ("%d",&n);
	for (int i=0;i<n;i++) {
		scanf ("%d",&a[i]); 
	}
	int m=1;
	h[1]=1;
	while (h[m]<n) h[++m]=3*h[m-1]+1;
	if (h[m]>n) m--;
	for (int i=1;i<=m;i++) {
		g[i]=h[m+1-i];
	}
	for (int i=1;i<=m;i++) {
		is (g[i]);
	}
	printf ("%d\n%d",m,g[1]);
	for (int i=2;i<=m;i++) {
		printf (" %d",g[i]);
	}
	printf ("\n%d\n",cnt);
	for (int i=0;i<n;i++) {
		printf ("%d\n",a[i]);
	}
    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 <cstdio>
using namespace std;
const int MAXN=1e6+7;
int n,cnt=0;
int a[MAXN],g[105],h[105];
void is (int g) {
	for (int i=g;i<n;i++) {
		int v=a[i],j=i-g;
		while (j>=0&&a[j]>v) {
			a[j+g]=a[j];
			j-=g;
			cnt++;
		}
		a[j+g]=v;
	}
}
int main () {
	scanf ("%d",&n);
	for (int i=0;i<n;i++) {
		scanf ("%d",&a[i]); 
	}
	int m=1;
	h[1]=1;
	while (h[m]<n) h[++m]=3*h[m-1]+1;
	if (h[m]>n) m--;
	for (int i=1;i<=m;i++) {
		g[i]=h[m+1-i];
	}
	for (int i=1;i<=m;i++) {
		is (g[i]);
	}
	printf ("%d\n%d",m,g[1]);
	for (int i=2;i<=m;i++) {
		printf (" %d",g[i]);
	}
	printf ("\n%d\n",cnt);
	for (int i=0;i<n;i++) {
		printf ("%d\n",a[i]);
	}
    return 0;
}

```