#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> adj[303];
vector<int> ch;
void dfs(int v) {
ch[v] = 1;
for (int u : adj[v]) {
if (ch[u]) continue;
dfs(u);
}
}
int other(int N, int v, int u) {
int ret = 0;
ch = vector<int>(N, 0);
ch[v] = ch[u] = 1;
for (int i = 0; i < N; i++) {
if (ch[i]) continue;
dfs(i);
ret++;
}
return ret;
}
int trivial(vector<int> E) {
int ret = 1;
for (int i = 1; i < E.size(); i++) if (E[i] != E[i-1]) ret++;
return ret;
}
vector<int> vec;
void solve(int s, int e, int x, int N, int r, int c) {
if (s == e) {
vec.push_back(3*s+r);
return;
}
int m = (s+e)/2;
vector<int> E(N, N);
for (int i = s; i <= m; i++) {
E[3*i+r] = -1;
E[3*i+r+1] = c;
}
int y = trivial(E) - perform_experiment(E);
if (y > 0) solve(s, m, y, N, r, c);
if (x-y > 0) solve(m+1, e, x-y, N, r, c);
}
vector<int> find_colours(int N, vector<int> X, vector<int> Y) {
for (int i = 0; i < X.size(); i++) {
adj[X[i]].push_back(Y[i]);
adj[Y[i]].push_back(X[i]);
}
vector<int> C(N, 0);
vector<int> color(N, 0);
for (int i = 0; i < N; i++) color[i] = i;
if (N <= 2) {
for (int i = 0; i < N; i++) {
vector<int> E(N, N);
E[i] = -1;
random_shuffle(color.begin(), color.end());
for (int j = 0; j < N; j++) {
E[adj[i][0]] = color[j];
int x = perform_experiment(E);
if (x - other(N, i, adj[i][0]) == 1) {
C[i] = color[j];
break;
}
}
}
}
else {
for (int r = 0; r < 3; r++) {
for (int j = 0; j < N; j++) {
vector<int> E(N, N);
int cnt = 0;
for (int i = 0; i < N-1; i++) {
if (i % 3 == r) {
E[i] = -1;
cnt++;
}
}
for (int i = 1; i < N; i++) {
if ((i - 1) % 3 == r) E[i] = color[j];
}
int x = trivial(E) - perform_experiment(E);
if (x > 0) solve(0, cnt-1, x, N, r, color[j]);
for (auto i : vec) C[i] = color[j];
vec.clear();
}
}
vector<int> E(N, N);
E[N-1] = -1;
random_shuffle(color.begin(), color.end());
for (int j = 0; j < N; j++) {
E[N-2] = color[j];
int x = perform_experiment(E);
if (x == 2) {
C[N-1] = color[j];
break;
}
}
}
return C;
}
