#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "longesttrip.h"
bool commonedge(VI a, VI b) {
return !are_connected(a, b);
}
bool commonedge(int u, int v) {
return !are_connected({u}, {v});
}
int n;
VVI gp;
VVI gpmatrix;
int mex(VI a) {
set<int> st;
for (int x : a) st.insert(x);
for (int i = 0; i < 2e9; i++) if (st.count(i) == 0) return i;
return -1;
}
VI longest_trip(int N, int D) {
/*if (D >= 2) {*/
/* int n = N;*/
/* VI group(n, -1);*/
/* int last = 0;*/
/* rep(u, n) if (group[u] == -1) {*/
/* group[u] = last;*/
/* rep(v, n) if (group[v] == -1) {*/
/* if (commonedge({u}, {v})) group[v] = last;*/
/* }*/
/* last++;*/
/* }*/
/* VVI comp(last);*/
/* rep(u, n) comp[group[u]].pb(u);*/
/* sort(all(comp), [&](const VI& a, const VI& b){return a.size() > b.size();});*/
/* int prev = -1;*/
/* VI ans;*/
/* rep(_, 3) {*/
/* rep(i, last) {*/
/* assert(comp[i].size() <= 2);*/
/* if (comp[i].size() && i != prev) {*/
/* ans.pb(comp[i].back());*/
/* comp[i].pop_back();*/
/* prev = i;*/
/* }*/
/* }*/
/* }*/
/* rep(i, last) assert(comp[i].size() == 0);*/
/* return ans;*/
/*}*/
n = N;
gp = VVI(n);
gpmatrix = VVI(n, VI(n));
replr(u, 0, n-1) {
replr(v, u+1, n-1) {
if (commonedge(u, v)) {
gp[u].pb(v);
gp[v].pb(u);
gpmatrix[u][v] = gpmatrix[v][u] = true;
/*cout << "found edge " << u << " " << v << endl;*/
}
}
}
VI vis(n);
VI group(n, -1);
int l = 0;
rep(u, n) {
VI ret;
for (int v : gp[u]) if (group[v] != -1) ret.pb(group[v]);
group[u] = mex(ret);
setmax(l, group[u]+1);
}
VVI comp(l);
rep(u, n) comp[group[u]].pb(u);
mt19937 rng(chrono::steady_clock().now().time_since_epoch().count());
for (VI& a : comp) shuffle(all(a), rng);
VI ans;
int prev = -1;
while (true) {
bool ayo = false;
for (VI& a : comp) {
VI nw;
for (int x : a) {
if (prev != -1 && gpmatrix[x][prev]) {
nw.pb(x);
continue;
}
ans.pb(x);
prev = x;
ayo = true;
}
a = nw;
}
if (ayo == false) break;
}
return ans;
/*vis = VI(l);*/
/*for (VI vec : comp) {*/
/* for (int x : vec) cout << x << " ";*/
/* cout << endl;*/
/*}*/
return {-1488};
}
