#include <bits/stdc++.h>
#include "split.h"
using namespace std;
typedef long long int lli;
typedef pair<int,int> pii;
typedef pair<lli,lli> pll;
const int MAXN=100000;
int ind[MAXN];
int low[MAXN];
int curind=1;
int subtreesize[MAXN];
vector<int> matrix[MAXN];
vector<int> dfsmatrix[MAXN];
pii need[3];
int purpletree;
vector<pii> redtrees;
int which[MAXN];
int needed;
bool bad=false;
void dfstarjan(int loc, int parent){
ind[loc]=curind;
low[loc]=curind++;
if(parent!=-1) {
dfsmatrix[loc].push_back(parent);
dfsmatrix[parent].push_back(loc);
}
for(int x:matrix[loc]){
if(!ind[x]){
dfstarjan(x,loc);
low[loc]=min(low[loc],low[x]);
}
else if(x!=parent)low[loc]=min(low[loc],ind[x]);
}
}
void findsizes(int loc, int parent, int above){
if(low[loc]<above&&ind[loc]!=above){
redtrees.push_back({loc,parent});
return;
}
purpletree+=1;
for(int x:dfsmatrix[loc]){
if(x!=parent)findsizes(x,loc,above);
}
}
void dfspurple(int loc, int parent, int toset, int above){
if(low[loc]<above&&ind[loc]!=above)return;
if(needed){
which[loc]=toset;
needed--;
if(needed)for(int x:dfsmatrix[loc])if(x!=parent)dfspurple(x,loc,toset,above);
}
}
void setred(int loc, int parent, int toset){
if(needed){
which[loc]=toset;
needed--;
if(needed)for(int x:dfsmatrix[loc])if(x!=parent)setred(x,loc,toset);
}
}
void dfsred(int loc, int parent, int toset, int above){
if(low[loc]<above&&ind[loc]!=above){
setred(loc,parent,toset);
return;
}
if(needed)for(int x:dfsmatrix[loc])if(x!=parent)dfsred(x,loc,toset,above);
}
void gendfs(int loc, int parent, int toset){
if(which[loc])return;
if(needed) {
which[loc] = toset;
needed--;
if(needed)for (int x:dfsmatrix[loc])if (x != parent)gendfs(x, loc, toset);
}
}
bool dfs(int loc, int parent){
subtreesize[loc]=1;
for(int x:dfsmatrix[loc]){
if(x!=parent){
bool done=dfs(x,loc);
if(done)return done;
else subtreesize[loc]+=subtreesize[x];
}
}
if(subtreesize[loc]>=need[0].first){
findsizes(loc,parent,ind[loc]);
if(purpletree>need[1].first+need[2].first){
bad=true;
return true;
}
if(purpletree>=need[1].first){
needed=need[1].first;
dfspurple(loc,parent,need[1].second,ind[loc]);
needed=need[0].first;
gendfs(0,-1,need[0].second);
return true;
}
if(purpletree>=need[0].first){
needed=need[0].first;
dfspurple(loc,parent,need[0].second,ind[loc]);
needed=need[1].first;
gendfs(0,-1,need[1].second);
return true;
}
needed=need[0].first;
dfspurple(loc,parent,need[0].second,ind[loc]);
dfsred(loc,parent,need[0].second,ind[loc]);
needed=need[1].first;
gendfs(0,-1,need[1].second);
return true;
}
return false;
}
vector<int> find_split(int n, int a, int b, int c, vector<int>p, vector<int>q) {
need[0]={a,1};
need[1]={b,2};
need[2]={c,3};
sort(need,need+3);
for(int i=0;i<p.size();i++){
matrix[p[i]].push_back(q[i]);
matrix[q[i]].push_back(p[i]);
}
dfstarjan(0,-1);
dfs(0,-1);
vector<int> ans;
for(int i=0;i<n;i++)ans.push_back(which[i]);
if(bad)return ans;
for(int i=0;i<n;i++){
if(!ans[i])ans[i]=need[2].second;
}
return ans;
}
//int main(){
// cin.tie(NULL);
// ios_base::sync_with_stdio(false);
// vector<int> p={0, 0, 0, 0, 0};
// vector<int> q={1, 2, 3, 4, 5};
// vector<int> ans=find_split(6, 2, 2, 2,p,q);
// for(int x:ans)printf("%d ",x);
// return 0;
//}
