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 <bits/stdc++.h>
using namespace std;

signed main(){
	int n,p[200];
	vector<int> ans;
	cin >> n;
	for(int i = 0;i < n;i++) cin >> p[i];
	for(int i = 0;i <= n;i++){
		for(int j = 0;j < n;j++){
			bool flag = true;
			for(int k = 0;k < n;k++){
				if(p[k] != k) flag = false;
			}
			if(flag){
				cout << ans.size() << endl;
				for(int v : ans) cout << v << endl;
				return 0;
			}
			if(j != n - 1 && p[0] < p[n - 1]){
				ans.push_back(n - 1);
				swap(p[0],p[n - 1]);
			}
			ans.push_back(1);
			for(int k = 1;k < n;k++) swap(p[k],p[k - 1]);
		}
	}
	return 0;
}