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 main() {
   ios_base::sync_with_stdio(false);
   int n;
   cin >> n;
   vector<int> p(n);
   for (int i = 0; i < n; ++i) {
      cin >> p[i];
   }
   auto finish = [&]() {
      for (int i = 0; i < n; ++i) {
         if (p[i] != i) return false;
      }
      return true;
   };
   vector<int> ans;
   auto go = [&](int k) {
      ans.push_back(k);
      for (int i = k; i < n; ++i) {
         swap(p[i], p[i - k]);
      }
   };
   while (!finish()) {
      if (p[0] < p[n - 1] && p[n - 1] != (n - 1)) {
         go(n - 1);
      } else {
         go(1);
      }
   }
   cout << ans.size() << "\n";
   for (int v : ans) {
      cout << v << "\n";
   }
}