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 maxn = 210;

int n,p[maxn];
vector<int> sol;

void swap(int &a,int &b) {
    int tg=a;
    a=b;
    b=tg;
}

void go(int k) {
    sol.push_back(k);
    for (int i=k;i<n;i++) swap(p[i],p[i-k]);
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>n;
    for (int i=0;i<n;i++) cin>>p[i];
    bool tested = true;
    while (tested) {
        tested = false;
        for (int i=0;i<n;i++) {
            if (p[0]!=0 && p[n-1] > p[0]) {
                tested = true;
                go(n-1);
            }
            go(1);
        }
      //  for (int i=0;i<n;i++) cout<<p[i]<<" ";
       // cout<<endl;
    }
    while (p[0]!=0) go(1);
    cout<<sol.size()<<endl;
    for (int i=0;i<sol.size();i++) cout<<sol[i]<<endl;
}