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:
/**
 *    author:  tourist
 *    created: 26.11.2019 11:33:34       
**/
#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<int> p(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
  }
  vector<int> seq;
  auto Do = [&](int k) {
    seq.push_back(k);
    for (int i = k; i < n; i++) {
      swap(p[i], p[i - k]);
    }
  };
  for (int it = 0; it < n - 1; it++) {
    Do(1);
    for (int i = 0; i < n - 1; i++) {
      if (p[n - 1] > p[0]) {
        Do(n - 1);
      }
      Do(1);
    }
  }
  for (int i = 0; i < n - 1; i++) {
    assert(p[i] < p[i + 1]);
  }
  cout << seq.size() << '\n';
  for (int x : seq) {
    cout << x << '\n';
  }
  return 0;
}