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;
typedef long long LL;

#ifdef BTK
#include<dvector.h>
#define DEBUG if(1)
#else
#define CIN_ONLY if(1)
struct cww{cww(){
    CIN_ONLY{
        ios::sync_with_stdio(false);cin.tie(0);
    }
}}star;
#define DEBUG if(0)
#endif

#define fin "\n"
#define FOR(i,bg,ed) for(int i=(bg);i<(ed);i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
#define pb push_back
#define REC(ret, ...) std::function<ret (__VA_ARGS__)>
template <typename T>inline bool chmin(T &l,T r)
{bool a=l>r;if(a)l=r;return a;}
template <typename T>inline bool chmax(T &l,T r)
{bool a=l<r;if(a)l=r;return a;}
template <typename T>
istream& operator>>(istream &is,vector<T> &v){
    for(auto &it:v)is>>it;
    return is;
}
int N;
typedef vector<int> V;
V ret;
int bg=0;

V f(V p,int k){
    FOR(i,k,N)swap(p[i],p[i-k]);
    return p;
}
V rt(V v){
    bg=(bg+1)%N;
    ret.pb(1);
    return f(v,1);
}
V sw(V v){
    ret.pb(N-1);
    return f(v,N-1);
}

bool check(V v){
    REP(i,N-1)if(v[i]>v[i+1])return false;
    return true;
}
typedef pair<int,V> X;
int main(){
    cin>>N;
    V in(N);
    REP(i,N)in[i]=N-i-1;
#ifndef BTK
    cin>>in;
#endif


    while(check(in)==false){
        if(bg==0)in=rt(in);
        else if(in.front()<in.back())in=sw(in);
        else in=rt(in);
    }
    
    cout<<ret.size()<<endl;
#ifndef BTK
    for(auto &it:ret)cout<<it<<endl;
#endif
    return 0;
}