#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ari2 = array<int, 2>;
using ari3 = array<int, 3>;
using arl2 = array<ll, 2>;
using arl3 = array<ll, 3>;
template <class T> using vt = vector<T>;
#define all(x) begin(x), end(x)
#define size(x) (int((x).size()))
#define REP(a,b,c,d) for(int a=(b);(d)>0?a<=(c):a>=(c);a+=(d))
#define FOR(a,b,c) REP(a,b,c,1)
#define ROF(a,b,c) REP(a,b,c,-1)
struct DSU {
vt<int> uf;
DSU(const int n) : uf(n, -1) {}
int find(const int i) { return uf[i] < 0 ? i : uf[i] = find(uf[i]); }
bool unite(int a, int b) {
if ((a = find(a)) == (b = find(b)))
return false;
if (uf[a] > uf[b])
swap(a, b);
uf[a] += uf[b];
uf[b] = a;
return true;
}
};
int query(const vt<int> &E) { return perform_experiment(E); }
vt<int> find_colours(const int N, const vt<int> X, const vt<int> Y) {
const int M = size(X);
if (N <= 50) {
vt<int> ret(N);
FOR(i, 0, N-1)
FOR(c, 0, N-1) {
vt<int> E(N, c);
E[i] = -1;
if (query(E) == 1) {
ret[i] = c;
break;
}
}
return ret;
}
if (M == N * (N - 1) / 2) {
vt<int> ret(N);
FOR(i, 0, N-1) {
int lo = 0, hi = N-1;
while (lo < hi) {
const int mid = lo + hi >> 1;
vt<int> E(N);
E[i] = -1;
int cur = 0;
FOR(j, 0, N-1)
if (j != i)
E[j] = min(cur++, mid);
if (query(E) > mid + 1)
lo = mid + 1;
else
hi = mid;
}
ret[i] = lo;
}
return ret;
}
bool sub3 = true;
FOR(i, 0, M - 1)
sub3 &= X[i] == i && Y[i] == i + 1;
if (sub3) {
vt<int> ans(N);
FOR(s, 0, 1) {
vt<int> test, subject;
REP(i, s, N - 1, 2)
test.push_back(i);
REP(i, !s, N - 1, 2)
subject.push_back(i);
FOR(c, 0, N - 1) {
int prv = -1;
while (prv + 1 < size(subject)) {
vt<int> E(N);
for (const auto &i : test)
E[i] = c;
FOR(i, 0, prv)
E[subject[i]] = N;
FOR(i, prv + 1, size(subject) - 1)
E[subject[i]] = -1;
if (query(E) == N)
break;
int lo = prv + 1, hi = size(subject) - 1;
while (lo < hi) {
const int mid = lo + hi >> 1;
FOR(i, prv + 1, mid)
E[subject[i]] = -1;
FOR(i, mid + 1, size(subject) - 1)
E[subject[i]] = N;
if (query(E) == N)
lo = mid + 1;
else
hi = mid;
}
ans[subject[lo]] = c;
prv = lo;
}
}
}
return ans;
}
vt<vt<int>> adj(N);
FOR(i, 0, M - 1) {
adj[X[i]].push_back(Y[i]);
adj[Y[i]].push_back(X[i]);
}
DSU uf(N);
const auto expect = [&](vt<int> E) {
FOR(i, 0, N - 1)
if (E[i] < 0)
E[i] = uf.find(i);
DSU uf2(N);
int ret = N;
FOR(i, 0, M - 1)
ret -= E[X[i]] == E[Y[i]] && uf2.unite(X[i], Y[i]);
assert(ret == query(E));
return ret;
};
int timer = 0;
vt<int> tin(N, -1), tout(N), rev_tin(N);
const auto dfs = [&](auto &&self, const int i) -> void {
rev_tin[tin[i] = timer++] = i;
vt<int> s_roots;
for (const auto &j : adj[i])
if (tin[j] < 0)
s_roots.push_back(j), self(self, j);
tout[i] = timer - 1;
vt<int> links;
for (const auto &j : s_roots) {
vt<int> comps;
FOR(k, tin[j], tout[j])
comps.push_back(uf.find(rev_tin[k]));
sort(all(comps));
comps.erase(unique(all(comps)), comps.end());
int prv = -1;
while (prv + 1 < size(comps)) {
vt<int> E(N, N);
E[i] = -1;
FOR(k, prv + 1, size(comps) - 1)
E[comps[k]] = -1;
FOR(k, 0, N - 1)
E[k] = E[uf.find(k)];
if (query(E) == expect(E))
break;
int lo = prv + 1, hi = size(comps) - 1;
while (lo < hi) {
const int mid = lo + hi >> 1;
FOR(k, prv + 1, mid)
E[comps[k]] = -1;
FOR(k, mid + 1, size(comps) - 1)
E[comps[k]] = N;
FOR(k, 0, N - 1)
E[k] = E[uf.find(k)];
if (query(E) == expect(E))
lo = mid + 1;
else
hi = mid;
}
links.push_back(comps[lo]);
prv = lo + 1;
}
}
for (const auto &j : links)
uf.unite(i, j);
};
dfs(dfs, 0);
vt<int> ans(N);
FOR(i, 0, N - 1)
ans[i] = uf.find(i);
return ans;
}
