#include <cstdio>
#include <vector>
using namespace std;

int cnt,m;
vector<int> G;

void insertionSort(vector<int>& a, int n, int g) {
	for(int i=g; i<n; ++i) {
		int j,v=a[i];
		for(j=i-g; j>=0 && a[j]>v;j-=g) {
			swap(a[j+g],a[j]);
			++cnt;
		}
		a[j+g]=v;
	}
}

void shellSort(vector<int>& a,int n) {
	cnt = 0;
	m=0;
	int d=n;
	G.resize(n);
	while(1) {
		d=2*d/3;
		if(d<2) {
			G[m]=d;
			++m;
			break;
		}
		G[m]=d;
		++m;
	}
	for(int i=0; i<m; ++i) {
		insertionSort(a, n, G[i]);
	}
}

int main() {
	int n;
	vector<int> a;
	scanf("%d",&n);
	a.resize(n);
	for(int i=0; i<n; ++i) {
		scanf("%d",&a[i]);
	}
	shellSort(a,n);
	printf("%d\n",m);
	for(int i=0; i<m-1; ++i) {
		printf("%d ",G[i]);
	}
	printf("%d\n%d\n",G[m-1],cnt);
	for(int i=0;i<n;++i) {
		printf("%d\n",a[i]);
	}
	return 0;
}
### Prompt

Your task is to create 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>
#include <vector>
using namespace std;

int cnt,m;
vector<int> G;

void insertionSort(vector<int>& a, int n, int g) {
	for(int i=g; i<n; ++i) {
		int j,v=a[i];
		for(j=i-g; j>=0 && a[j]>v;j-=g) {
			swap(a[j+g],a[j]);
			++cnt;
		}
		a[j+g]=v;
	}
}

void shellSort(vector<int>& a,int n) {
	cnt = 0;
	m=0;
	int d=n;
	G.resize(n);
	while(1) {
		d=2*d/3;
		if(d<2) {
			G[m]=d;
			++m;
			break;
		}
		G[m]=d;
		++m;
	}
	for(int i=0; i<m; ++i) {
		insertionSort(a, n, G[i]);
	}
}

int main() {
	int n;
	vector<int> a;
	scanf("%d",&n);
	a.resize(n);
	for(int i=0; i<n; ++i) {
		scanf("%d",&a[i]);
	}
	shellSort(a,n);
	printf("%d\n",m);
	for(int i=0; i<m-1; ++i) {
		printf("%d ",G[i]);
	}
	printf("%d\n%d\n",G[m-1],cnt);
	for(int i=0;i<n;++i) {
		printf("%d\n",a[i]);
	}
	return 0;
}
```