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(){
    int N;
    cin >> N;
    vector<int> A(N), B(N);
    for(int i=0; i<N; i++){
        cin >> A[i];
        B[i] = A[i];
    }

    vector<int> ans;
    for(int i=0; i<N-1; i++){
        ans.push_back(1);
        rotate(A.begin(), A.begin()+1, A.end());
        for(int j=0; j<N-1; j++){
            if(A[0] < A.back()){
                ans.push_back(N-1);
                swap(A[0], A.back());
            }
            ans.push_back(1);
            rotate(A.begin(), A.begin()+1, A.end());
        }
    }

    cout << ans.size() << endl;
    for(int a : ans) cout << a << endl;

    // for(int a : ans){
    //     for(int i=a; i<N; i++) swap(B[i], B[i-a]);
    // }
    // for(int i=0; i<N; i++) cerr << B[i] << " ";
    return 0;
}