#include<bits/stdc++.h>
#include "interactive.h"
#define pii pair<int,int>
// #define int long long
using namespace std;
const int inf=0x7fffffff,mod=1e9+7,N=5e2+10;
int n;
int e[N][N];
int q3(int x,int y,int z){
    vector<int>vec;
    vec.clear();
    vec.push_back(x);vec.push_back(y);vec.push_back(z);
    for(int i=1;i<=n;++i)if(i!=x&&i!=y&&i!=z)vec.push_back(i);
    return query(vec);
}
void lk(int u,int v,int k){
    e[u][v]=e[v][u]=k;
}
void get_one(int x,int y,int z){
    //  f1=yz-xz               f2=yz-xy               f3=xy-xz
    int f1=q3(x,y,z)-q3(y,x,z),f2=q3(x,z,y)-q3(z,x,y),f3=f1-f2;
    if(f1==1)
        lk(y,z,1),lk(x,y,f2==0);
    else if(f1==-1)
        lk(x,z,1),lk(x,y,f3==0);
    if(f2==1)
        lk(y,z,1),lk(x,z,f1==0);
    else if(f2==-1)
        lk(x,y,1),lk(x,z,f3==0);
    if(f3==1)
        lk(x,y,1),lk(y,z,f2==0);
    else if(f3==-1)
        lk(x,z,1),lk(y,z,f1==0);
}
bool book[N];
int work(int l,int r,int d){
    // cerr<<l<<" "<<r<<" "<<d<<'\n';
    int res=0;
    vector<int>vec;
    vec.clear();
    for(int i=1;i<=n;++i)book[i]=0;
    for(int i=2;i<l;++i)vec.push_back(i);
    for(int i=l;i<=min(r+d,n);++i){
        if(book[i])continue;
        if(i&1){
            int tmp=i;
            while(tmp+d<=min(r+d,n))tmp+=d;
            while(tmp>=i){
                vec.push_back(tmp);
                book[tmp]=1;
                tmp-=d;
            }
        }else
            for(int tmp=i;tmp<=min(r+d,n);tmp+=d){
                vec.push_back(tmp);
                book[tmp]=1;
            }
    }
    for(int i=min(r+d,n);i>=r+1;--i)if(!book[i])vec.push_back(i);
    vec.push_back(1);
    for(int i=r+d+1;i<=n;++i)vec.push_back(i);
    // for(auto x:vec)cerr<<x<<" ";
    // cerr<<'\n';
    res=query(vec);
    for(int i=1;i<vec.size();++i)res-=e[vec[i]][vec[i-1]];
    // cerr<<res<<'\n';
    return res;
}
void calc(int l,int r,int d,int tmp){
    if(!tmp)return;
    if(l==r)return lk(l,l+d,1),void();
    int mid=(l+r)>>1,res=work(l,mid,d);
    calc(l,mid,d,res);
    calc(mid+1,r,d,tmp-res);
}
bool vis[N];
vector<int>solve(int m){
    vector<int>ans;
    n=m; 
    //cerr << "CHECKIN\n";
    for(int i=2;i<n;++i)get_one(1,i,i+1);
    // cerr << "CHECKIN\n";
    for(int i=2;i<=n;++i)calc(2,n,i,work(2,n,i));
    // cerr << "CHECKIN\n";
    int st=0;
    for(int i=1;i<=n;++i){
        int du=0;
        for(int j=1;j<=n;++j)du+=e[i][j];
        if(du==1)st=i;
    }
    while(st!=n+1){
        vis[st]=1;
        ans.push_back(st);
        int nxt=0;
        for(nxt=1;nxt<=n&&(vis[nxt]||!e[st][nxt]);++nxt);
        st=nxt;
    }
    // cerr << "ANS SIZE : " << ans.size() << "\n";
    return ans;
}