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<cstdio>
#include<algorithm>
using namespace std;
int n, w[310], R[101000], RC;
void Rotate(int K){
	R[RC++] = K;
	for (int i = K; i < n; i++)swap(w[i - K], w[i]);
}
int main() {
	int i, j;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%d", &w[i]);
	}
	for (i = 1; i < n; i++) {
		for (j = 0; j < n - i; j++) {
			if (w[0] < w[n - 1]) Rotate(n-1);
			Rotate(1);
		}
		for (j = 0; j < i - 1; j++)Rotate(1);
		if (i != n - 1)Rotate(1);
	}
	printf("%d\n", RC);
	for (i = 0; i < RC; i++)printf("%d\n", R[i]);
}