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;

const int N = 205;

int n, a[N];

vector<int> ans;

void op (int X) {
	ans.push_back(X);
	for(int i=X;i<n;i++) {
		swap(a[i], a[i-X]);
	}
}

int main()
{
	scanf("%d",&n);
	for(int i=0;i<n;i++) {
		scanf("%d",&a[i]);
	}
	while(a[n-1] != 0) {
		op(1);
	}
	for(int i=1;i<n;i++) {
		while(a[n-1] != i) {
			op(1);
		}
		while(a[n-2] != i-1) {
			op(n-1);
			op(1);
		}
	}
	printf("%d\n",(int)ans.size());
	for(auto &T : ans) {
		printf("%d\n",T);
	}
}