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 <iostream>
#include <fstream>
#include <cassert>
#include <typeinfo>
#include <vector>
#include <stack>
#include <cmath>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <iomanip>
#include <cctype>
#include <random>
#include <complex>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<long double,long double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<long double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<pll,ll> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<62;
const double pi=acos(-1);
const long double eps=1e-7;
const ll mod=1e6+3;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,0};

int n;
vi a,b,c;
vi res;

void f(int k){
	assert(0<k&&k<n);
	for(int i=k;i<n;i++){
		swap(a[i],a[i-k]);
		swap(b[a[i]],b[a[i-k]]);
	}
	res.push_back(k);
}

void Open(){
	for(int i=0;i<n;i++) cout<<a[i]<<' ';
	cout<<endl;
}

int main(){
	cin>>n;
	a=b=c=vi(n);
	int N=n/2;
	for(int i=0;i<n;i++){
		cin>>a[i];
		b[a[i]]=i;
		c[i]=abs(N-i);
		if(n%2==0&&i<N) c[i]--;
	}
	if(n%2==1) while(a[N]!=N) f(1);
	for(int i=0;i<N;i++){
		int L=N-i-1,R=N+i+n%2;
		if(c[b[L]]!=c[b[R]]){
			int x=(c[b[L]]<c[b[R]]?L:R),y=L+R-x;
			f(N+c[b[x]]);
			if((b[L]<N)^(b[R]<N)) f(n-1);
			f(N+c[b[y]]+1);
			bool B=b[x]>=N,T=n%2==0&&!i;
			while(B&&b[y]||!B&&b[y]!=n-1) f(1);
			f(n-1);
			while(T&&c[b[x]]!=c[b[y]]||!T&&a[N]!=N) f(1);
		}
		f(max(b[L],b[R]));
		if(b[R]) f(n-1);
		f(R);
	}
	int S=res.size();
	cout<<S<<endl;
	for(int i=0;i<S;i++) cout<<res[i]<<endl;
}