#include<iostream>
#include<vector>

int main(){
    using namespace std;
    
    vector<size_t> G{2391484, 797161, 265720, 88573, 29524, 9841, 3280, 1093, 364, 121, 40, 13, 4, 1};
    
    // input
    size_t n;
    cin >> n;
    vector<unsigned long> A(n);
    for(auto& i : A)cin >> i;
    if(n == 1)return 0 & puts("1\n1\n0\n1");
    
    // process
    unsigned long cnt{0};
    cout << lower_bound(G.rbegin(), G.rend(), n) - G.rbegin() << endl;
    for(const auto& g : G)if(g < n){
        cout << g << " \n"[g == 1];
        for(size_t i = g; i < n; ++i)for(size_t j = i; j >= g && A[j - g] > A[j]; j -= g, ++cnt)swap(A[j], A[j - g]);
    }
    cout << cnt << endl;
    for(const auto& a : A)cout << a << endl;
}

### Prompt

Please formulate 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<vector>

int main(){
    using namespace std;
    
    vector<size_t> G{2391484, 797161, 265720, 88573, 29524, 9841, 3280, 1093, 364, 121, 40, 13, 4, 1};
    
    // input
    size_t n;
    cin >> n;
    vector<unsigned long> A(n);
    for(auto& i : A)cin >> i;
    if(n == 1)return 0 & puts("1\n1\n0\n1");
    
    // process
    unsigned long cnt{0};
    cout << lower_bound(G.rbegin(), G.rend(), n) - G.rbegin() << endl;
    for(const auto& g : G)if(g < n){
        cout << g << " \n"[g == 1];
        for(size_t i = g; i < n; ++i)for(size_t j = i; j >= g && A[j - g] > A[j]; j -= g, ++cnt)swap(A[j], A[j - g]);
    }
    cout << cnt << endl;
    for(const auto& a : A)cout << a << endl;
}

```