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>
#include<algorithm>
using namespace std;
int N;
int p[200];
vector<int>ans;
int main()
{
	cin>>N;
	for(int i=0;i<N;i++)cin>>p[i];
	int hd=0;
	while(ans.size()<=1e5)
	{
		bool issorted=true;
		for(int i=0;i<N;i++)if(p[(hd+i)%N]!=i)
		{
			issorted=false;
			break;
		}
		if(issorted)break;
		if(p[hd]!=0&&p[hd]<p[(hd+N-1)%N])
		{
			ans.push_back(N-1);
			swap(p[hd],p[(hd+N-1)%N]);
		}
		ans.push_back(1);
		hd=(hd+1)%N;
	}
	if(ans.size()>1e5)return 1;
	cout<<ans.size()<<endl;
	for(int v:ans)cout<<v<<endl;
}