Problem:
Score : 400 points

Problem Statement

There are N cities. There are also K roads and L railways, extending between the cities.
The i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.
No two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.

We will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.
We will also define connectivity by railways similarly.

For each city, find the number of the cities connected to that city by both roads and railways.

Constraints

2 ≦ N ≦ 2*10^5

1 ≦ K, L≦ 10^5

1 ≦ p_i, q_i, r_i, s_i ≦ N

p_i < q_i

r_i < s_i

When i ≠ j, (p_i, q_i) ≠ (p_j, q_j)

When i ≠ j, (r_i, s_i) ≠ (r_j, s_j)

Input

The input is given from Standard Input in the following format:

N K L
p_1 q_1
:
p_K q_K
r_1 s_1
:
r_L s_L

Output

Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.

Sample Input 1

4 3 1
1 2
2 3
3 4
2 3

Sample Output 1

1 2 2 1

All the four cities are connected to each other by roads.

By railways, only the second and third cities are connected. Thus, the answers for the cities are 1, 2, 2 and 1, respectively.

Sample Input 2

4 2 2
1 2
2 3
1 4
2 3

Sample Output 2

1 2 2 1

Sample Input 3

7 4 4
1 2
2 3
2 5
6 7
3 5
4 5
3 4
6 7

Sample Output 3

1 1 2 1 2 2 2

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

    public void Proc()
    {
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
        int matiCount = inpt[0];
        int roadCount = inpt[1];
        int railCount = inpt[2];

        this.RoadMatiList = new TreeNode[matiCount];
        this.RailMatiList = new TreeNode[matiCount];

        for (int i = 0; i < roadCount; i++) {
            inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a) - 1).ToArray();
            if(!Road.ContainsKey(inpt[0])) {
                Road.Add(inpt[0], new Dictionary<int, bool>());
            }
            if(!this.Road.ContainsKey(inpt[1])) {
                this.Road.Add(inpt[1], new Dictionary<int, bool>());
            }
            this.Road[inpt[0]][inpt[1]] = true;
            this.Road[inpt[1]][inpt[0]] = true;
        }
        for (int i = 0; i < railCount; i++) {
            inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a) - 1).ToArray();
            if(!this.Rail.ContainsKey(inpt[0])) {
                this.Rail.Add(inpt[0], new Dictionary<int, bool>());
            }
            if(!this.Rail.ContainsKey(inpt[1])) {
                this.Rail.Add(inpt[1], new Dictionary<int, bool>());
            }
            this.Rail[inpt[0]][inpt[1]] = true;
            this.Rail[inpt[1]][inpt[0]] = true;
        }
        for (int i = 0; i < matiCount; i++) {
            if(this.RoadMatiList[i] != null) {
                continue;
            }
            this.RoadMatiList[i] = new TreeNode(i);
            Queue<TreeNode> que = new Queue<TreeNode>();
            que.Enqueue(this.RoadMatiList[i]);
            while(que.Count>0) {
                TreeNode curr = que.Dequeue();
                if(!this.Road.ContainsKey(curr.ID)) {
                    continue;
                }
                foreach(int next in this.Road[curr.ID].Keys) {
                    if(curr.Parent != null && curr.Parent.ID==next) {
                        continue;
                    }
                    if(RoadMatiList[next] != null) {
                        continue;
                    }
                    RoadMatiList[next] = curr.AddChild(next);
                    que.Enqueue(RoadMatiList[next]);
                }
            }
        }
        for (int i = 0; i < matiCount; i++) {
            if(this.RailMatiList[i] != null) {
                continue;
            }
            this.RailMatiList[i] = new TreeNode(i);
            Queue<TreeNode> que = new Queue<TreeNode>();
            que.Enqueue(this.RailMatiList[i]);
            while(que.Count>0) {
                TreeNode curr = que.Dequeue();
                if(!this.Rail.ContainsKey(curr.ID)) {
                    continue;
                }
                foreach(int next in this.Rail[curr.ID].Keys) {
                    if(RailMatiList[next]!=null) {
                        continue;
                    }
                    RailMatiList[next] = curr.AddChild(next);
                    que.Enqueue(RailMatiList[next]);
                }
            }
        }

        Dictionary<int, Dictionary<int, int>> groupCount = new Dictionary<int, Dictionary<int, int>>();
        for (int i = 0; i < matiCount; i++) {
            int roadGroup = this.RoadMatiList[i].Root.ID;
            int railGroup = this.RailMatiList[i].Root.ID;
            if(!groupCount.ContainsKey(roadGroup)) {
                groupCount.Add(roadGroup, new Dictionary<int, int>());
            }
            if(groupCount[roadGroup].ContainsKey(railGroup)) {
                groupCount[roadGroup][railGroup]++;
            } else {
                groupCount[roadGroup][railGroup] = 1;
            }
        }

        int[] cnt = new int[matiCount];
        for (int i = 0; i < matiCount; i++) {
            int roadGroup = this.RoadMatiList[i].Root.ID;
            int railGroup = this.RailMatiList[i].Root.ID;
            cnt[i] = groupCount[roadGroup][railGroup];
        }
        string ans = string.Join(" ", cnt);
        Console.WriteLine(ans);
    }

    private TreeNode[] RoadMatiList;
    private TreeNode[] RailMatiList;

    private Dictionary<int, Dictionary<int, bool>> Road = new Dictionary<int, Dictionary<int, bool>>();
    private Dictionary<int, Dictionary<int, bool>> Rail = new Dictionary<int, Dictionary<int, bool>>();

    private class TreeNode {
        public TreeNode Parent;
        public TreeNode Root;
        public List<TreeNode> Items = new List<TreeNode>();
        public int ID;
        public TreeNode(int id) {
            this.ID = id;
            this.Root = this;
        }
        public TreeNode AddChild(int id) {
            TreeNode tn = new TreeNode(id);
            this.Items.Add(tn);
            tn.Parent = this;
            if(this.Parent==null) {
                tn.Root = this;
            } else {
                tn.Root = this.Root;
            }
            return tn;
        }
        public TreeNode AddChild(TreeNode target) {
            this.Items.Add(target);
            target.Parent = this;
            if(this.Parent==null) {
                target.Root = this;
            } else {
                target.Root = this.Root;
            }
            return target;
        }
    }




    public class Reader
    {
        private static StringReader sr;
        public static bool IsDebug = false;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (sr == null)
                {
                    sr = new StringReader(InputText.Trim());
                }
                return sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
        private static string InputText = @"




7 4 4
1 2
2 3
2 5
6 7
3 5
4 5
3 4
6 7


";
    }

    public static void Main(string[] args)
    {
#if DEBUG
        Reader.IsDebug = true;
#endif
        Program prg = new Program();
        prg.Proc();
    }
}