import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
//IOI 2019
//Split
//Current Version: 31 May 2019
//Mahdi Safarnejad Boroujeni
class Pair implements Comparable<Pair> {
final int first, second;
Pair(int first, int second) {
this.first=first;
this.second=second;
}
@Override
public int compareTo(Pair b) {
if (first!=b.first)
return first - b.first;
return second - b.second;
}
}
public class split {
int n;
List<Integer>[] a;
ArrayList<Pair> b;
int[] result, mark, size, startingtime, mintime;
int counter = 1;
boolean finishedPhase1 = false;
int dfs2(int v, int goal, int comp, boolean ignore_st) {
int sum=1;
mark[v]=2;
result[v]=comp;
goal -= 1;
for (int i = 0; i < a[v].size(); i++)
if (goal > 0 && mark[a[v].get(i)] < 2 && (ignore_st || (startingtime[a[v].get(i)] > startingtime[v]))) {
int thisSize = dfs2(a[v].get(i), goal, comp, ignore_st);
sum += thisSize;
goal -= thisSize;
}
return sum;
}
void dfs(int v, int par) {
mark[v]=1;
size[v]=1;
startingtime[v] = counter++;
mintime[v] = startingtime[v];
int removablesSum=0;
for (int i = 0; i < a[v].size(); i++)
if (mark[a[v].get(i)] == 0){
dfs(a[v].get(i), v);
if (finishedPhase1)
return;
size[v]+=size[a[v].get(i)];
mintime[v] = Math.min(mintime[v], mintime[a[v].get(i)]);
if (mintime[a[v].get(i)] < startingtime[v])
removablesSum += size[a[v].get(i)];
} else if (a[v].get(i)!=par) {
mintime[v] = Math.min(mintime[v], mintime[a[v].get(i)]);
}
if (size[v] >= b.get(0).first) {
finishedPhase1 = true;
if (n - size[v] + removablesSum < b.get(0).first)
return; //No Solution
int element = 0;
if (n - size[v] + removablesSum < b.get(1).first)
element = 1;
result[v] = b.get(element).second;
mark[v]=2;
int goal = b.get(element).first - 1;
for (int i = 0; i < a[v].size(); i++) {
if (mark[a[v].get(i)] < 2 && goal > 0 && mintime[a[v].get(i)] >= startingtime[v] && startingtime[a[v].get(i)] > startingtime[v])
goal -= dfs2(a[v].get(i), goal, b.get(element).second, false);
}
for (int i = 0; i < a[v].size(); i++) {
if (mark[a[v].get(i)] < 2 && goal > 0 && mintime[a[v].get(i)] < startingtime[v] && startingtime[a[v].get(i)] > startingtime[v])
goal -= dfs2(a[v].get(i), goal, b.get(element).second, false);
}
dfs2(0, b.get(1-element).first, b.get(1-element).second, true);
for (int i = 0; i < n; i++)
if (result[i]==0)
result[i]=b.get(2).second;
}
}
public int[] find_split(int n, int a_, int b_, int c_, int[] p, int[] q) {
this.n = n;
result = new int[n];
mark = new int[n];
size = new int[n];
startingtime = new int[n];
mintime = new int[n];
a = new ArrayList[n];
for (int i = 0; i < n; i++)
a[i] = new ArrayList<Integer>();
b = new ArrayList<Pair>();
b.add(new Pair(a_, 1));
b.add(new Pair(b_, 2));
b.add(new Pair(c_, 3));
Collections.sort(b);
for (int i = 0; i < p.length; i++) {
a[p[i]].add(q[i]);
a[q[i]].add(p[i]);
}
dfs(0, -1);
return result;
}
// public static void main(String[] args) {
// split test = new split();
// int[] p = {0, 0, 0};
// int[] q = {1, 2, 3};
// int[] result = test.do_split(4, 2, 1, 1, p, q);
// for (int i = 0; i < 4; i++)
// System.out.print(result[i]+" ");
// System.out.println();
// }
}
