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 <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int n, p[209], q[209];
int main() {
	cin >> n;
	for (int i = 0; i < n; i++) cin >> p[i], q[i] = p[i];
	vector<int> v;
	int cyclic = 0;
	while (true) {
		bool flag = false;
		for (int i = 1; i < n; i++) {
			if (p[i - 1] > p[i]) {
				flag = true;
				int tp = i - cyclic;
				if (tp < 0) tp += n;
				for (int j = 0; j < tp; j++) v.push_back(1);
				cyclic = (cyclic + tp) % n;
				v.push_back(n - 1);
				swap(p[i], p[i - 1]);
			}
		}
		if (!flag) break;
	}
	while (cyclic % n != 0) cyclic++, v.push_back(1);
	cout << v.size() << endl;
	for (int i : v) {
		cout << i << endl;
		for (int j = i; j < n; j++) {
			swap(q[j - i], q[j]);
		}
	}
	return 0;
}