Shell Sort is a generalization of Insertion Sort to arrange a list of nn elements AA .

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 gg -th elements. Beginning with large values of gg , it repeats the insertion sort with smaller gg .

Your task is to complete the above program by filling ?. Write a program which reads an integer nn and a sequence AA , and prints mm , Gi(i=0,1,...,m−1)Gi(i=0,1,...,m−1) in the pseudo code and the sequence AA in ascending order. The output of your program must meet the following requirements:

• 1≤m≤1001≤m≤100
• 0≤Gi≤n0≤Gi≤n
• cnt does not exceed ⌈n1.5⌉⌈n1.5⌉

Input

In the first line, an integer nn is given. In the following nn lines, Ai(i=0,1,...,n−1)Ai(i=0,1,...,n−1) are given for each line.

Output

In the first line, print an integer mm . In the second line, print mm integers Gi(i=0,1,...,m−1)Gi(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 nn lines, print Ai(i=0,1,...,n−1)Ai(i=0,1,...,n−1) respectively.

This problem has multiple solutions and the judge will be performed by a special validator.

Constraints

• 1≤n≤1,000,0001≤n≤1,000,000
• 0≤Ai≤1090≤Ai≤109

Sample Input 1

5
5
1
4
3
2

Sample Output 1

2
4 1
3
1
2
3
4
5

Sample Input 2

3
3
2
1

Sample Output 2

1
1
3
1
2
3

程式碼如下：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;
const int maxn=1000005;
int n;
int a[maxn];
int cnt;
vector<int> G;
void InsertSort (int g)
{
    for (int i=g;i<n;i++)
    {
        int temp=a[i];
        int loc=i-g;
        while (loc>=0&&a[loc]>temp)
        {
            a[loc+g]=a[loc];
            loc-=g;
            cnt++;
        }
        a[loc+g]=temp;
    }
}
void ShellSort ()
{
    int h=1;
    while (h<=n)
    {
        G.push_back(h);
        h=3*h+1;
    }
    for (int i=G.size()-1;i>=0;i--)
    {
        InsertSort(G[i]);
    }
}
int main()
{
    scanf("%d",&n);
    for (int i=0;i<n;i++)
          scanf("%d",&a[i]);
    cnt=0;
    ShellSort();
    printf("%d\n",G.size());
    for (int i=G.size()-1;i>=0;i--)
        printf("%d%c",G[i],i==0? '\n':' ');
        printf("%d\n",cnt);
    for (int i=0;i<n;i++)
        printf("%d\n",a[i]);
    return 0;
}