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>
using namespace std;

int n, a[209]; vector<int>X;

bool isperm() {
	for (int i = 0; i < n; i++) { if (a[i] != i) return false; }
	return true;
}
void shuffle(int p) {
	for (int i = p; i < n; i++) swap(a[i], a[i - p]);
}
bool perm(int p, int q) {
	if (q >= 1 && p < q) return true;
	if (q == 0 && p > q) return true;
	return false;
}

int main() {
	cin >> n;
	for (int i = 0; i < n; i++) cin >> a[i];
	while (true) {
		if (isperm() == true) break;
		if (perm(a[n - 1], a[0]) == false) { X.push_back(n - 1); shuffle(n - 1); }
		else { X.push_back(1); shuffle(1); }
	}
	cout << X.size() << endl;
	for (int i = 0; i < X.size(); i++)cout << X[i] << endl;
	return 0;
}