#include <bits/stdc++.h>
using namespace std;
int perform_experiment(vector<int> e);
vector<int>alll(int n,vector<int> x,vector<int> y){
vector<int>color(n);
for(int i=0;i<n;i++){
vector<int>nodos;
for(int j=0;j<n;j++){
if(j!=i){
nodos.push_back(j);
}
}
int l=0,r=n-1;
while(l<r){
int mid=(l+r)/2;
vector<int>exp(n,l);
exp[i]=-1;
int node=0;
for(int j=l;j<=mid;j++){
exp[nodos[node]]=j;
node++;
}
int experimento=perform_experiment(exp);
if(experimento==(mid-l+1)){
r=mid;
}
else{
l=mid+1;
}
}
color[i]=l;
}
return color;
}
vector<int> uno(int n, vector<int>& x, vector<int>& y) {
vector<int> color(n, -1);
vector<vector<int>> adj(n);
for (int i = 0; i < x.size(); i++) {
adj[x[i]].push_back(y[i]);
adj[y[i]].push_back(x[i]);
}
color[0] = 0;
queue<int> q;
q.push(0);
while (!q.empty()) {
int curr = q.front(); q.pop();
for (int neighbor : adj[curr]) {
if (color[neighbor] == -1) {
vector<int> exp(n, -1);
exp[curr] = color[curr];
exp[neighbor] = !color[curr];
int result = perform_experiment(exp);
color[neighbor] = (result == 1) ? color[curr] : !color[curr];
q.push(neighbor);
}
}
}
return color;
}
vector<int> find_colours(int n,vector<int> x,vector<int> y){
vector<int>grado(n,0);
for(int i=0;i<x.size();i++){
grado[x[i]]++;
grado[y[i]]++;
}
bool all=true;
for(int i=0;i<n;i++){
if(grado[i]!=(n-1)){
all=false;
}
}
if(n<=50){
vector<int> color(n, -1);
for (int i = 0; i < n; ++i) {
for (int c = 0; c < n; ++c){
vector<int> e(n, c); e[i] = -1;
int foo = perform_experiment(e);
if (foo == 1) {
color[i] = c;
break;
}
}
}
return color;
}
if(all){
return alll(n,x,y);
}
return uno(n,x,y);
}
