#include "split.h"
#include <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
#define pb push_back
#define sz(x) (int)(x).size()
const int mx = 100005;
int n;
bool SUB1 = 1;
bool SUB2 = 1;
bool SUB3 = 1;
bool SUB4 = 1;
vi adj[mx];
vi res;
int sub[mx];
int par[mx];
vi children[mx];
void genSub(int node, int prv = -1){
sub[node] = 1;
for(auto u: adj[node]){
if(u == prv) continue;
children[node].pb(u);
par[u] = node;
genSub(u, node);
sub[node]+=sub[u];
}
}
int cnt;
void makeSub(int node, int num, int id){
if(num != -1){
cnt = num;
makeSub(node, -1, id);
return;
}
if(cnt == 0) return;
res[node] = id;
cnt--;
for(auto u: children[node]) makeSub(u, -1, id);
}
void makenSub(int node, int num, int id, int prv = -1){
//cout << node << " " << num << " " << id << " " << prv << "\n";
if(num != -1){
cnt = num;
makenSub(node, -1, id, prv);
return;
}
if(cnt == 0) return;
res[node] = id;
cnt--;
if(node != 0 && par[node] != prv) makenSub(par[node], -1, id, node);
for(auto u: children[node]) if(u != prv) makenSub(u, -1, id, node);
}
vi find_split(int _n, int a, int b, int c, vi p, vi q) {
n = _n;
res = vi(n, 0);
for(int i = 0; i < sz(p); i++){
adj[p[i]].pb(q[i]);
adj[q[i]].pb(p[i]);
}
for(int i = 0; i < n; i++){
if(sz(adj[i]) > 2) SUB1 = 0;
}
if(a != 1) SUB2 = 0;
if(sz(p) != n-1) SUB3 = 0;
if(n > 2500 || sz(p) > 5000) SUB4 = 0;
if(SUB1){
int A = 0;
int B = 0;
int C = 0;
int cur = 0;
for(int i = 0; i < n; i++) if(sz(adj[i]) == 1) cur = i;
int last = -1;
while(true){
if(A < a){
res[cur] = 1;
A++;
}
else if(B < b){
res[cur] = 2;
B++;
}
else if(C < c){
res[cur] = 3;
C++;
}
else break;
if(adj[cur][0] == last){
if(sz(adj[cur]) == 1) break;
last = cur;
cur = adj[cur][1];
}
else{
last = cur;
cur = adj[cur][0];
}
}
return res;
}
if(SUB2){
vi inComp(n, 0);
queue<int> q;
int B = 0;
inComp[0] = 1;
B++;
q.push(0);
while(sz(q)){
int node = q.front();
q.pop();
for(auto u: adj[node]) if(inComp[u] == 0 && B < b){
inComp[u] = 1;
B++;
q.push(u);
}
if(B == b) break;
}
for(int i = 0; i < n; i++) if(inComp[i] == 1) res[i] = 2;
for(int i = 0; i < n; i++){
if(inComp[i] == 0){
res[i] = 1;
break;
}
}
for(int i = 0; i < n; i++) if(res[i] == 0) res[i] = 3;
return res;
}
if(SUB3){
genSub(0);
for(int i = 0; i < n; i++){
if(a <= sub[i] && min(b, c) <= n-sub[i]){
//cout << i << "1\n";
makeSub(i, a, 1);
if(b <= c){
makenSub(par[i], b, 2, i);
}
else{
makenSub(par[i], c, 3, i);
}
break;
}
if(b <= sub[i] && min(a, c) <= n-sub[i]){
//cout << i << "2\n";
makeSub(i, b, 2);
if(a <= c){
makenSub(par[i], a, 1, i);
}
else{
makenSub(par[i], c, 3, i);
}
break;
}
if(c <= sub[i] && min(a, b) <= n-sub[i]){
//cout << i << "3\n";
makeSub(i, c, 3);
if(a <= b){
makenSub(par[i], a, 1, i);
}
else{
makenSub(par[i], b, 2, i);
}
break;
}
}
vi full(4, 0);
for(int i = 0; i < n; i++) full[res[i]] = 1;
if(full[1] == 0 && full[2] == 0 && full[3] == 0){
return res;
}
for(int i = 1; i <= 3; i++) if(full[i] == 0){
for(int j = 0; j < n; j++){
if(res[j] == 0) res[j] = i;
}
}
return res;
}
return res;
}
