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:
//冷静に考えるとk=1, n-1しか必要なくて、数列を回しながらバブルソートするだけ。
#include <iostream>
#include <vector>
#define rep(i, n) for(i = 0; i < n; i++)
using namespace std;

int n;
int p[200];
vector<int> ans;

int main() {
	int i, j;
	
	cin >> n;
	rep(i, n - 1) cin >> p[i + 1];
	cin >> p[0];
	
	rep(i, n) {
		int hanten = 0;
		for (j = 0; j < n - 1; j++) {
			if (p[j] > p[j + 1]) {
				swap(p[j], p[j + 1]);
				ans.push_back(n - 1);
				hanten++;
			}
			ans.push_back(1);
		}
		if (hanten == 0) break;
		ans.push_back(1);
	}
	
	cout << ans.size() << endl;
	rep(i, ans.size()) {
		cout << ans[i] << endl;
	}
	return 0;
}