#include <bits/stdc++.h>
using namespace std;
int perform_experiment(vector<int> E);
int n;
vector<vector<int>> adj;
int query(const vector<int> &c) {
if (find(c.begin(), c.end(), -1) != c.end()) {
return perform_experiment(c);
}
int ans = 0;
queue<int> q;
vector<bool> vis(n);
for (int i = 0; i < n; ++i) {
if (vis[i]) {
continue;
}
vis[i] = true;
ans++;
q.push(i);
while (!q.empty()) {
int u = q.front();
q.pop();
for (int &i : adj[u]) {
if (!vis[i] and c[u] == c[i]) {
vis[i] = true;
q.push(i);
}
}
}
}
return ans;
}
class dsu {
private:
int n;
vector<int> par, size;
vector<vector<int>> comp_m;
public:
dsu(int n) : n(n), par(n), size(n, 1), comp_m(n) {
iota(par.begin(), par.end(), 0);
for (int i = 0; i < n; ++i) {
comp_m[i].push_back(i);
}
}
int root(int u) { return u == par[u] ? u : par[u] = root(par[u]); }
void merge(int u, int v) {
u = root(u), v = root(v);
if (u == v) {
return;
}
if (size[u] < size[v]) {
swap(u, v);
}
for (int &i : comp_m[v]) {
comp_m[u].push_back(i);
}
par[v] = u;
size[u] += size[v];
}
const vector<int> &comp(int u) { return comp_m[root(u)]; }
};
vector<int> find_colours(int N, vector<int> x, vector<int> y) {
n = N;
adj.resize(n);
for (int i = 0; i < x.size(); ++i) {
adj[x[i]].push_back(y[i]), adj[y[i]].push_back(x[i]);
}
dsu dsu(n);
for (int u = 1; u < n; ++u) {
vector<char> seen(n);
vector<int> nodes;
for (int &i : adj[u]) {
if (int r = dsu.root(i); r <= u && !exchange(seen[r], true)) {
nodes.push_back(r);
}
}
auto has = [&](int from, int till) {
vector<int> q(n, n);
for (int i = from; i <= till; ++i) {
for (int u : dsu.comp(nodes[i])) {
q[u] = dsu.root(nodes[i]);
}
}
q[u] = n + 1;
int bef = query(q);
for (int i = from; i <= till; ++i) {
for (int u : dsu.comp(nodes[i])) {
q[u] = -1;
}
}
q[u] = -1;
return bef - query(q);
};
for (int _ = 0, times = has(0, nodes.size() - 1), fr = -1; _ < times; ++_) {
dsu.merge(u, nodes[fr = *ranges::partition_point(views::iota(fr + 1, int(nodes.size()) - 1), [&](int i) { return !has(fr + 1, i); })]);
}
}
vector<vector<int>> nadj(n);
for (int u = 0; u < n; ++u) {
for (int &i : adj[u]) {
if (dsu.root(u) != dsu.root(i)) {
nadj[dsu.root(u)].push_back(dsu.root(i));
}
}
}
for (int u = 0; u < n; ++u) {
sort(nadj[u].begin(), nadj[u].end());
nadj[u].erase(unique(nadj[u].begin(), nadj[u].end()), nadj[u].end());
}
vector<int> dist(n);
queue<int> q;
vector<bool> vis(n);
for (int i = 0; i < n; ++i) {
if (vis[i] or dsu.root(i) != i) {
continue;
}
vis[i] = true;
q.push(i);
while (!q.empty()) {
int u = q.front();
q.pop();
for (int &i : nadj[u]) {
if (!vis[i]) {
vis[i] = true;
dist[i] = dist[u] + 1;
q.push(i);
}
}
}
}
vector<int> a, b;
for (int u = 0; u < n; ++u) {
if (dsu.root(u) != u) {
continue;
}
(dist[u] & 1 ? a : b).push_back(u);
}
vector<int> ans(n);
if (a.empty()) {
for (int c = 0; c < n; ++c) {
vector<int> q(n, -1);
q[0] = c;
if (query(q) == 1) {
ans[b[0]] = c;
break;
}
}
} else {
for (auto &[a, b] : array<pair<vector<int>, vector<int>>, 2>({{a, b}, {b, a}})) {
for (int c = 0; c < n; c++) {
int qq = -1;
auto has = [&](int from, int till, bool setqq = false) {
vector<int> q(n, n);
for (int &i : b) {
for (auto &u : dsu.comp(i)) {
q[u] = n + 1;
}
}
for (int i = from; i <= till; ++i) {
for (auto &u : dsu.comp(a[i])) {
q[u] = a[i];
}
}
int bef = query(q);
for (int &i : b) {
for (auto &u : dsu.comp(i)) {
q[u] = c;
}
}
for (int i = from; i <= till; ++i) {
for (auto &u : dsu.comp(a[i])) {
q[u] = -1;
}
}
int aft = query(q);
if (setqq) {
qq = bef - aft;
}
return bef - aft;
};
int fr = -1;
while (true) {
if (qq == 0) {
break;
}
if (has(fr + 1, a.size() - 1, true) == 0) {
break;
}
int rr = 0;
fr = *ranges::partition_point(views::iota(fr + 1, int(a.size()) - 1), [&](int i) {
int v = has(fr + 1, i);
if (v != 0) {
rr = v;
}
return v == 0;
});
qq -= rr;
ans[a[fr]] = c;
}
}
}
}
for (int i = 0; i < n; ++i) {
ans[i] = ans[dsu.root(i)];
}
return ans;
}
