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;

vector <int> V;
int A[222];
int n;

int main()
{
	int i, j, t;
	
	scanf("%d", &n);
	
	for(i=1; i<=n; i++){
		scanf("%d", A+i);
	}
	
	for(i=1; i<=n; i++){
		t = 1;
		for(j=1; j<n; j++){
			if(A[j] > A[j+1]){
				for(; t<j+1; t++) V.push_back(1);
				swap(A[j], A[j+1]);
				V.push_back(n - 1);
			}
		}
		for(; t<=n; t++) V.push_back(1);
	}
	
	printf("%d\n", (int)V.size());
	
	for(int t: V) printf("%d\n", t);
	
	return 0;
}