Problem: Snuke has a sequence p, which is a permutation of (0,1,2, ...,N-1). The i-th element (0-indexed) in p is p_i.

He can perform N-1 kinds of operations labeled 1,2,...,N-1 any number of times in any order. When the operation labeled k is executed, the procedure represented by the following code will be performed:


for(int i=k;i<N;i++)
swap(p[i],p[i-k]);


He would like to sort p in increasing order using between 0 and 10^{5} operations (inclusive). Show one such sequence of operations. It can be proved that there always exists such a sequence of operations under the constraints in this problem.

Constraints

* 2 \leq N \leq 200
* 0 \leq p_i \leq N-1
* p is a permutation of (0,1,2,...,N-1).

Input

Input is given from Standard Input in the following format:


N
p_0 p_1 ... p_{N-1}


Output

Let m be the number of operations in your solution. In the first line, print m. In the i-th of the following m lines, print the label of the i-th executed operation. The solution will be accepted if m is at most 10^5 and p is in increasing order after the execution of the m operations.

Examples

Input

5
4 2 0 1 3


Output

4
2
3
1
2


Input

9
1 0 4 3 5 6 2 8 7


Output

11
3
6
1
3
5
2
4
7
8
6
3

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
using namespace std;

const int N = 205;
int n, a[N];
vector<int> ans;

bool sorted(int n, int a[])
{
    for (int i = 0; i < n-1; i++)
        if (a[i] > a[i+1])
        return 0;
    return 1;
}
int main()
{
    cin >> n;
    for (int i = 0; i < n; i++)
        cin >> a[i];
    while(!sorted(n,a))
    {
        if (a[0] < a[n-1] && a[n-1] != n-1)
        {
            ans.push_back(n-1);
            swap(a[0],a[n-1]);
        }
        ans.push_back(1);
        for (int i = 0; i < n-1; i++)
        {
            swap(a[i],a[i+1]);
        }
    }
    cout << ans.size() << endl;
    for (auto x: ans)
        cout << x << endl;
}