#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
using vi =vector<int>;
using vvi =vector<vi>;
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define all(x) (x).begin(), (x).end()
#define bg(x) (x).begin()
#define en(x) (x).end()
#define sz(x) int((x).size())
#define rev(x) reverse(all(x))
#define srt(x) sort(all(x))
#define each(a, x) for (auto &a : x)
#define trace(x) for (auto &el : x) cout << el << " "
struct DSU {
int n; vi par, siz;
DSU() {};
DSU(int N) {
n = N; siz.assign(n, 1);
par.resize(n); iota(all(par), 0);
}
int find(int v) {
if (par[v] == v) return v;
return par[v] = find(par[v]);
}
void unite(int a, int b) {
a = find(a); b = find(b);
if (a != b) {
if (siz[b] > siz[a]) swap(a, b);
par[b] = a; siz[a] += siz[b];
}
}
};
int n, m;
vi x, y;
vvi adj;
vi even_to(int x, int col) {
vi to_ret(n, n);
for (int i = 0; i < n; i+=2) to_ret[i] = -1;
if (x == 0) {
to_ret[2] = n;
to_ret[1] = col;
} else {
for (int i = 0; i <= x; i++) {
to_ret[2*i + 1] = col;
}
}
return to_ret;
}
vi odd_to(int x, int col) {
vi to_ret(n, n);
for (int i = 1; i < n; i += 2) to_ret[i] = -1;
FOR(i, 0, x+1) to_ret[2*i+1] = col;
return to_ret;
}
int count_components(vi &graph) {
int cmps = 0;
vector<bool> seen(n, false);
FOR(i, 0, n) {
if (seen[i]) continue;
seen[i] = true;
queue<int> q; q.push(i);
while (!q.empty()) {
int cur = q.front();
q.pop();
for (auto &v : adj[cur]) {
if (seen[v]) continue;
if (graph[v] != graph[cur]) continue;
seen[v] = true;
q.push(v);
}
}
cmps++;
}
return cmps;
}
vi find_colours(int N, vi X, vi Y) {
n = N; m = sz(X); x = X; y = Y;
adj.assign(n, vi());
FOR(i, 0, m) adj[x[i]].pb(y[i]), adj[y[i]].pb(x[i]);
vi graph(n, n); iota(graph.begin(), graph.end(), 0);
if (n == 2) {
graph[0] = perform_experiment({-1, 0}) == 1 ? 0 : 1;
graph[1] = perform_experiment({0, -1}) == 1 ? 0 : 1;
return graph;
}
auto dsu = DSU(n);
FOR(i, 0, n-1) {
vi test(n, n);
test[i] = test[i+1] = -1;
int perf = perform_experiment(test);
if ((i == 0 || i == n - 2) && perf == 2) {
dsu.unite(i, i+1);
} else if (!(i == 0 || i == n - 2) && perf == 3) {
dsu.unite(i, i+1);
}
}
FOR(col, 0, n) {
FOR(even_idx, 0, (n+1)/2) {
vi even = even_to(even_idx, col);
if (perform_experiment(even) != count_components(even)) {
graph[dsu.find(2*even_idx)] = col;
}
}
FOR(odd_idx, 0, n/2) {
vi odd = odd_to(odd_idx, col);
if (perform_experiment(odd) != count_components(odd)) {
graph[dsu.find(2*odd_idx+1)] = col;
}
}
}
FOR(i, 0, n) {
graph[i] = graph[dsu.find(i)];
}
return graph;
}
