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;
int n,a[101000],c[101000],tp;
bool chk(){
	for(int i=2;i<=n;++i)if(a[i]<a[i-1])return false;
	return true;
}
void rot(){
	c[++tp]=1;
	int x=a[1];
	for(int i=1;i<n;++i)a[i]=a[i+1];
	a[n]=x;
}
void sp(){
	c[++tp]=n-1;
	swap(a[1],a[n]);
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
		scanf("%d",&a[i]),a[i]++;
	for(int i=1;i<=n;++i){
		while(a[n]!=i)rot();
		while(a[n-1]!=i-1&&i>1)sp(),rot();
	}
	printf("%d\n",tp);
	for(int i=1;i<=tp;++i)printf("%d\n",c[i]);
}