#include<bits/stdc++.h>
using namespace std;
#include "sphinx.h"
int n,m;
vector<int>C,G;
int fa[255],u[100005],v[100005];
int findfather(int x){
	return x==fa[x]?x:fa[x]=findfather(fa[x]);
}
int aa[255];
int findaa(int x){
	return x==aa[x]?x:aa[x]=findaa(aa[x]);
}
bool fff=0;int ct=0;
int qqq(std::vector<int> x) {
	ct++;
	assert(ct<=2500);
	int tx=perform_experiment(x);
	return tx;
}
vector<int>gg[255];
int ss[255],vist[255],tt,I;
int query(int l,int r){
	for(int i=0;i<n;++i)vist[i]=0,aa[i]=i,C[i]=n;
	for(int i=l;i<=r;++i)for(auto cu:gg[ss[i]])vist[cu]=1,C[cu]=-1;
	vist[I]=1,C[I]=-1;
	for(int i=0;i<m;++i)if(!vist[u[i]]&&!vist[v[i]]){
		int fu=findaa(u[i]),fv=findaa(v[i]);
		if(fu!=fv)aa[fu]=fv;
	}
	int cnt=0;
	for(int i=0;i<n;++i)if(!vist[i]&&aa[i]==i)++cnt;
	return r-l+1+1+cnt-qqq(C);
}
double ef=0.382;
long double f[1009];
int f2[1009];
void solve(int l,int r,int k){
	if(!k)return;
	if(l==r){
		fa[ss[l]]=I;
		return;
	}
	int mid=l+f2[r-l+1]-1;
	int k1=query(l,mid);
	solve(l,mid,k1);
	solve(mid+1,r,k-k1);
}
int s1[255],s2[255];
vector<int>g[255];
int dep[255];
void dfs(int x){
	vist[x]=1;
	for(auto cu:g[x])if(!vist[cu]){
		dep[cu]=dep[x]+1;
		dfs(cu);
	}
}
int p[255],v1[255],v2[255],ss1[255],ss2[255];
int query1(int l,int r,int d){
	if(l>r) return 0;
	for(int i=0;i<n;++i)vist[i]=0,aa[i]=i,C[i]=d;
	for(int i=l;i<=r;++i)for(auto cu:gg[ss1[i]])vist[cu]=1,C[cu]=-1;
	for(int i=0;i<m;++i)if(!vist[u[i]]&&!vist[v[i]]){
		int fu=findaa(u[i]),fv=findaa(v[i]);
		if(fu!=fv)aa[fu]=fv;
	}
	int cnt=0;
	for(int i=0;i<n;++i)if(!vist[i]&&aa[i]==i)++cnt;
	if(cnt==1||fff) return r-l+1+cnt-qqq(C);
	else if(r-l+1+cnt-qqq(C)) return -1;
	else return 0;
}
int query2(int l,int r,int d){
	if(l>r) return 0;
	for(int i=0;i<n;++i)vist[i]=0,aa[i]=i,C[i]=d;
	for(int i=l;i<=r;++i)for(auto cu:gg[ss2[i]])vist[cu]=1,C[cu]=-1;
	for(int i=0;i<m;++i)if(!vist[u[i]]&&!vist[v[i]]){
		int fu=findaa(u[i]),fv=findaa(v[i]);
		if(fu!=fv)aa[fu]=fv;
	}
	int cnt=0;
	for(int i=0;i<n;++i)if(!vist[i]&&aa[i]==i)++cnt;
	if(cnt==1||fff) return r-l+1+cnt-qqq(C);
	else if(r-l+1+cnt-qqq(C)) return -1;
	else return 0;
}
void solve1(int l,int r,int d,int k){
	if(k==0) return;
	if(l==r){
		G[ss1[l]]=d;v1[ss1[l]]=1;
		return;
	}
	int mid=l+f2[r-l+1]-1;
	int f1=query1(l,mid,d);
	if(0==f1){
		if(k!=-1&&f1!=-1) k-=f1;else k=-1; 
		solve1(mid+1,r,d,k);
	}else{
		solve1(l,mid,d,f1);
		if(k!=-1&&f1!=-1) k-=f1;else k=query1(mid+1,r,d); 
		solve1(mid+1,r,d,k);
	}
}
void solve2(int l,int r,int d,int k){
	if(k==0) return;
	if(l==r){
		G[ss2[l]]=d;v2[ss2[l]]=1;
		return;
	}
	int mid=l+f2[r-l+1]-1;
	int f1=query2(l,mid,d);
	if(0==f1){
		if(k!=-1&&f1!=-1) k-=f1;else k=-1; 
		solve2(mid+1,r,d,k);
	}else{
		solve2(l,mid,d,f1);
		if(k!=-1&&f1!=-1) k-=f1;else k=query2(mid+1,r,d); 
		solve2(mid+1,r,d,k);
	}
}
vector<int>find_colours(int N,vector<int>X,vector<int>Y){
	for(int i=2;i<=250;i++) {
		f[i]=114514;
		for(int j=1;j<i;j++) {
			if(f[i]>(f[j]*j+f[i-j]*(i-j)+(i+j))/i) {
				f[i]=(f[j]*j+f[i-j]*(i-j)+(i+j))/i;
				f2[i]=j;
			}
		}
	//	printf("%.12Lf %d\n",f[i],f2[i]);
	}
	long double as=1;
	for(int i=1;i<=125;i++) as+=f[i]+1;
	//printf("%.12Lf\n",as*2);
	n=N;m=X.size();
	C.resize(n);G.resize(n);
	for(int i=0;i<m;++i){
		u[i]=X[i],v[i]=Y[i];
	}
	for(int i=0;i<n;++i)fa[i]=i;
	for(int i=0;i<n;++i)p[i]=i;
	mt19937 mt(time(0));
	if(m>n-1) {
		shuffle(p,p+n,mt);
		for(int x=1;x<n;++x){
			int i=p[x];
			I=i;
			for(int j=0;j<x;++j)gg[p[j]].clear();
			for(int j=0;j<x;++j){
				gg[findfather(p[j])].emplace_back(p[j]);
			}
			tt=0;
			for(int j=0;j<x;++j)if(gg[p[j]].size())ss[++tt]=p[j];
			solve(1,tt,query(1,tt));
		}
	} else fff=1;
	for(int j=0;j<n;++j)gg[j].clear();
	for(int j=0;j<n;++j){
		gg[findfather(j)].emplace_back(j);
	}
	for(int i=0;i<n;++i)g[i].clear();
	for(int i=0;i<m;++i)if(findfather(u[i])!=findfather(v[i])){
		int fu=fa[u[i]],fv=fa[v[i]];
		g[fu].emplace_back(fv);
		g[fv].emplace_back(fu);
	}
	int r=findfather(0);
	for(int i=0;i<n;++i)vist[i]=0;
	dep[r]=0;dfs(r);
	int t1=0,t2=0;
	for(int i=0;i<n;++i)if(fa[i]==i){
		if(dep[i]%2)s1[++t1]=i;
		else s2[++t2]=i;
	}
	if(t1+t2==1){
		for(int i=0;i<n;++i){
			for(int j=0;j<n;++j)G[j]=(j==0?-1:i);
			if(qqq(G)==1){
				for(int j=0;j<n;++j)G[j]=i;
				break;
			}
		}
		return G;
	}
	for(int i=0;i<n;++i)v1[i]=v2[i]=0;
	for(int i=0;i<n;++i)p[i]=i;
	shuffle(p,p+n,mt);
	for(int dd=0;dd<n;++dd){
		int d=p[dd];
		int tt1=0,tt2=0;
		for(int i=1;i<=t1;++i)if(!v1[s1[i]]){
			ss1[++tt1]=s1[i];
		}
		for(int i=1;i<=t2;++i)if(!v2[s2[i]]){
			ss2[++tt2]=s2[i];
		}
		shuffle(ss1+1,ss1+tt1+1,mt);
		shuffle(ss2+1,ss2+tt2+1,mt);
		if(tt1)solve1(1,tt1,d,query1(1,tt1,d));
		if(tt2)solve2(1,tt2,d,query2(1,tt2,d));
	}
	if(fff) for(int i=0;i<n;i++) G[i]=fa[i];
	else for(int i=0;i<n;++i)G[i]=G[fa[i]];
	return G;
}