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;
using Int = long long;
//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  vector<Int> p(n);
  for(Int i=0;i<n;i++) cin>>p[i];

  vector<Int> ans;
  auto mov=
    [&](Int k){
      if(k==0||k==n) return;
      ans.emplace_back(k);
      for(Int i=k;i<n;i++)
	swap(p[i],p[i-k]);
    };

  for(Int t=0;t<n;t++){
    mov(1);
    for(Int i=1;i<n;i++){
      if(p[0]<p[n-1]) mov(n-1);
      mov(1);
    }
  }
  
  assert(is_sorted(p.begin(),p.end()));
  cout<<ans.size()<<endl;
  for(Int x:ans) cout<<x<<endl;
  return 0;
}