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;
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n; cin >> n;
	vector<int> a(n), ops;
	for(int & v : a) cin >> v;
	auto sorted = [&](){
		for(int k = 0; k < n; k++){
			int i;
			for(i = 0; i < n - 1; i++) if(a[(i + k) % n] > a[(i + 1 + k) % n]) break;
			if(i == n - 1) return k;
		}
		return -1;
	};
	auto op = [&](int k){
		ops.push_back(k);
		for(int i = k; i < n; i++)
			swap(a[i], a[i - k]);
	};
	for(int i = 0; i < n && sorted() == -1; i++){
		for(int j = 0; j < n - 1; j++){
			op(1);
			if(a[0] < a[n - 1]) op(n - 1);
		}
		op(1);
	}
	while(sorted() != 0) op(1);
	cout << ops.size() << '\n';
	for(int v : ops) cout << v << '\n';
	return 0;
}