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;
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define _repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define _rep(i,n) _repl(i,0,n)
#define rep(...) GET_MACRO(__VA_ARGS__, _repl, _rep)(__VA_ARGS__)
#define mp(a,b) make_pair((a),(b))
#define pb(a) push_back((a))
#define all(x) (x).begin(),(x).end()
#define uniq(x) sort(all(x)),(x).erase(unique(all(x)),end(x))
#define fi first
#define se second
#define dbg(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
void _dbg(string){cout<<endl;}
template<class H,class... T> void _dbg(string s,H h,T... t){int l=s.find(',');cout<<s.substr(0,l)<<" = "<<h<<", ";_dbg(s.substr(l+1),t...);}
template<class T,class U> ostream& operator<<(ostream &o, const pair<T,U> &p){o<<"("<<p.fi<<","<<p.se<<")";return o;}
template<class T> ostream& operator<<(ostream &o, const vector<T> &v){o<<"[";for(T t:v){o<<t<<",";}o<<"]";return o;}

#define INF 1120000000
#define long long long // for codeforces

int n;
vector<int> ans;

void exec(int k, int l){
  if(k+1 == l) return;

  rep(i,k) ans.pb(1);
  rep(i,l-k-1){
    ans.pb(1);
    ans.pb(n-1);
  }
  rep(i, n-l+1) ans.pb(1);
}

int main(){
  cin>>n;
  vector<int> v(n);
  rep(i,n) cin>>v[i];

  int done = 0;
  while(done<n){
    int key = 0;
    rep(i,n-done) if(v[i] > v[key]) key = i;
    exec(key, n-done);
    rep(i, key, n-done-1) swap(v[i], v[i+1]);
    done++;
    // dbg(v);
    // dbg(ans);
  }

  cout << ans.size() << "\n";
  for(auto i : ans) cout << i << "\n";

  return 0;
}