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;

typedef long long ll;
typedef pair<int, int> PII;
#define pb push_back

#define N 210
int n, a[N];
vector<int> A;

void rot(int k) {
	if (k == 0) return;
	A.pb(k);
	for (int i = k; i < n; i ++) swap(a[i], a[i-k]);
}

int main() {
	cin >> n;
	for (int i = 0; i < n; i ++) cin >> a[i];
	while (true) {
		bool F = false;
		for (int i = 0; i < n; i ++) {
			if (a[0] != 0 && a[n-1] > a[0]) {
				F = true;
				rot(n-1);
			}
			rot(1);
		}
		if (!F) break;
	}
	while (a[0] != 0) rot(1);
	printf ("%d\n", (int) A.size());
	for (int i = 0; i < (int) A.size(); i ++)
		cout << A[i] << endl;
	for (int i = 0; i < n; i ++) assert(a[i] == i);
	return 0;
}