#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef pair<int,int> pi;
typedef vector<pi> pii;
typedef tuple<int,int,int> ti;
typedef vector<ll> li;
typedef vector<li> lii;
#define REP(i,a,b) for(int i=a;i<b;i++)
#define F first
#define S second
#define PB push_back
#define LSOne(s) ((s)&(-s))
#define all(x) (x).begin(),(x).end()
ll INF=1000000000000000010;
int inf=1e9+10;
ll M=1e9+7;
vi p,s,brr;
int n;
vii a;
int parent(int x){
if(p[x]==x)return x;
return p[x]=parent(p[x]);
}
void merge(int x,int y){
x=parent(x);
y=parent(y);
if(x==y)return;
if(s[x]<s[y])swap(x,y);
s[x]+=s[y];
p[y]=x;
}
void dfs(int x,vi &vis){
vis[x]=1;
for(auto u:a[x])if(!vis[u])dfs(u,vis);
}
void solve(int l,int r,vi &arr,int sz,int x){
if(sz==0)return;
if(l==r){
merge(x,arr[l]);
return;
}
int m=(l+r)/2;
vi b(n,n);
b[x]=-1;
REP(i,0,m+1)b[arr[i]]=-1;
int k=perform_experiment(b);
vi vis(n,0);
vis[x]=1;
REP(i,0,m+1)vis[arr[i]]=1;
int tot=m-l+2;
REP(j,0,n)if(!vis[j]){
tot++;
dfs(j,vis);
}
int y=tot-k;
solve(l,m,arr,y,x);
solve(m+1,r,arr,sz-y,x);
}
std::vector<int> find_colours(int N, std::vector<int> X, std::vector<int> Y) {
n=N;
a.resize(n);
REP(i,0,X.size()){
a[X[i]].PB(Y[i]);
a[Y[i]].PB(X[i]);
}
p.resize(n);s.resize(n,1);
REP(i,0,n)p[i]=i;
vi pr(n,0);
REP(i,0,n){
vi dn(n,0);
vi arr;
for(auto u:a[i])if(pr[parent(u)]&&!dn[parent(u)]){
dn[parent(u)]=1;
arr.PB(u);
}
pr[i]=1;
if(arr.empty())continue;
vi b(n,n);
for(auto u:arr)b[u]=-1;
b[i]=-1;
int k=perform_experiment(b);
vi vis(n,0);
vis[i]=1;
for(auto u:arr)vis[u]=1;
int tot=arr.size()+1;
REP(j,0,n)if(!vis[j]){
tot++;
dfs(j,vis);
}
solve(0,(int)arr.size()-1,arr,tot-k,i);
}
vi ans(n,-1);
int cl=0;
REP(i,0,n)if(ans[i]==-1){
if(ans[parent(i)]==-1)ans[parent(i)]=cl++;
ans[i]=ans[parent(i)];
}
return ans;
}
