/*************************************
* author: marvinthang *
* created: 06.09.2024 18:06:34 *
*************************************/
#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left___
#define right ___right___
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#ifdef LOCAL
#include "debug.h"
#else
#define DB(...)
#define db(...) ""
#define debug(...)
#endif
namespace std {
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream &print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class...U> print_op(tuple <U...>) { return print_tuple_utils<0, tuple <U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))>typename enable_if <!is_same<Con, string>::value, ostream &>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
template <class T> print_op(stack <T>) { vector <T> v; stack <T> st = u; while (!st.empty()) v.push_back(st.top()), st.pop(); reverse(v.begin(), v.end()); return out << v; }
template <class T> print_op(queue <T>) { queue <T> q = u; out << '{'; while (!q.empty()) { out << q.front(); q.pop(); if (!q.empty()) out << ", "; } out << '}'; return out; }
template <class T, class X, class Y> print_op(priority_queue <T, X, Y>) { priority_queue <T, X, Y> pq = u; out << '{'; while (!pq.empty()) { out << pq.top(); pq.pop(); if (!pq.empty()) out << ", "; } out << '}'; return out; }
template <class Fun> class y_combinator_result { Fun fun_; public: template <class T> explicit y_combinator_result(T &&fun): fun_(forward<T>(fun)) {} template <class...Args> decltype(auto)operator()(Args &&...args) { return fun_(ref(*this), forward<Args>(args)...); } };
template <class Fun> decltype(auto)y_combinator(Fun &&fun) { return y_combinator_result<decay_t<Fun>>(forward<Fun>(fun)); }
template <typename T, int D> struct Vec: public vector <Vec<T, D - 1>> { static_assert(D >= 1, "Vector dimension must be greater than zero!"); template <typename ...Args> Vec(int n = 0, Args ...args): vector <Vec<T, D - 1>>(n, Vec<T, D - 1>(args...)) {} };
template <typename T> struct Vec<T, 1>: public vector<T>{ Vec(int n = 0, const T &val = T()): vector<T>(n, val) {} };
#if __cplusplus < 202002L
template <class T> int ssize(const T &a) { return a.size(); }
#endif
}
vector <int> find_colours(int n, vector <int> X, vector <int> Y) {
int m = X.size();
Vec <int, 2> adj(n);
for (int i = 0; i < m; ++i) {
adj[X[i]].push_back(Y[i]);
adj[Y[i]].push_back(X[i]);
}
auto get_ncompx = [&] (const vector <int> &E, int x) {
queue <int> q;
int cnt = 0;
vector <bool> visited(n);
for (int i = 0; i < n; ++i) if (!visited[i] && E[i] == x) {
++cnt;
visited[i] = true;
q.push(i);
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v: adj[u]) if (!visited[v] && E[v] == x) {
visited[v] = true;
q.push(v);
}
}
}
return cnt;
};
auto ask_ncomp = [&] (vector <int> E) {
return perform_experiment(E) - get_ncompx(E, n);
};
vector <int> comp(n, -1);
int ncomp = 0;
vector <int> E(n, n);
for (int u = 0; u < n; ++u) {
E[u] = -1;
int new_ncomp = ask_ncomp(E);
if (ncomp < new_ncomp) {
comp[u] = ncomp;
} else {
Vec <int, 2> lst(ncomp);
int first = -1;
for (int i = 0; i < u; ++i) lst[comp[i]].push_back(i);
for (int t = 0, lt = 0; t <= ncomp - new_ncomp; ++t) {
auto check = [&] (int i) {
vector <int> E(n, n);
E[u] = -1;
for (int j = lt; j <= i; ++j) for (auto u: lst[j]) E[u] = -1;
int actual = ask_ncomp(E);
int expected = i - lt + 2;
return actual < expected;
};
int l = lt, r = ncomp - 2;
while (l <= r) {
int m = (l + r) >> 1;
if (check(m)) r = m - 1;
else l = m + 1;
}
if (first == -1) {
comp[u] = first = l;
} else {
for (int i = 0; i < n; ++i) if (comp[i] > comp[lst[l][0]]) --comp[i];
for (int u: lst[l]) comp[u] = first;
}
lt = l + 1;
}
}
ncomp = new_ncomp;
}
Vec <int, 2> cadj(ncomp);
for (int i = 0; i < m; ++i) {
X[i] = comp[X[i]];
Y[i] = comp[Y[i]];
cadj[X[i]].push_back(Y[i]);
cadj[Y[i]].push_back(X[i]);
}
vector <int> f(ncomp, -1);
queue <int> q;
q.push(0);
f[0] = 0;
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v: cadj[u]) if (f[v] == -1) {
f[v] = !f[u];
q.push(v);
}
}
Vec <int, 2> list_f(2), list_comp(ncomp);
for (int i = 0; i < n; ++i) list_comp[comp[i]].push_back(i);
for (int i = 0; i < ncomp; ++i) list_f[f[i]].push_back(i);
vector <int> comp_color(ncomp, -1);
if (ncomp == 1) {
for (int c = 0; c < n; ++c) {
vector <int> E(n, c);
E[0] = -1;
if (ask_ncomp(E) == 1) {
comp_color[0] = c;
break;
}
}
} else {
for (int t = 0; t < 2; ++t) {
for (int c = 0; c < n && !list_f[t].empty(); ++c) {
int rt = ssize(list_f[t]);
auto check = [&] (int i) {
vector <int> E(n, c);
for (int j = i + 1; j < rt; ++j) {
for (int u: list_comp[list_f[t][j]]) E[u] = -1;
}
int actual = ask_ncomp(E);
int expected = rt - i - 1 + get_ncompx(E, c);
return actual == expected;
};
while (!check(-1)) {
int l = 0, r = rt - 2;
while (l <= r) {
int m = (l + r) >> 1;
if (check(m)) r = m - 1;
else l = m + 1;
}
comp_color[list_f[t][l]] = c;
list_f[t].erase(list_f[t].begin() + l);
rt = l;
}
}
}
}
vector <int> res(n);
for (int i = 0; i < n; ++i) res[i] = comp_color[comp[i]];
return res;
}
