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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("4 3 1");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("3 4");
            WillReturn.Add("2 3");
            //1 2 2 1
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("4 2 2");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("1 4");
            WillReturn.Add("2 3");
            //1 2 2 1
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("7 4 4");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("2 5");
            WillReturn.Add("6 7");
            WillReturn.Add("3 5");
            WillReturn.Add("4 5");
            WillReturn.Add("3 4");
            WillReturn.Add("6 7");
            //1 1 2 1 2 2 2
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] wkArr = InputList[0].Split(' ').Select(X => int.Parse(X)).ToArray();
        int N = wkArr[0];
        int K = wkArr[1];
        int L = wkArr[2];

        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        //道路のUnionFind木
        var DouroTree = new List<HashSet<int>>();
        for (int I = 1; I <= K; I++) {
            SplitAct(InputList[I]);
            RenketuSyori(DouroTree, wkArr[0], wkArr[1]);
        }

        //鉄道のUnionFind
        var TetudouTree = new List<HashSet<int>>();
        for (int I = K + 1; I <= K + L; I++) {
            SplitAct(InputList[I]);
            RenketuSyori(TetudouTree, wkArr[0], wkArr[1]);
        }

        for (int I = 1; I <= N; I++) {
            int wkInd1 = DouroTree.FindIndex(X => X.Contains(I));
            int wkInd2 = TetudouTree.FindIndex(X => X.Contains(I));

            if (wkInd1 == -1 || wkInd2 == -1) {
                Console.WriteLine(1);
            }
            else {
                Console.WriteLine(DouroTree[wkInd1].Intersect(TetudouTree[wkInd2]).Count());
            }
        }
    }

    //連結処理を行う
    static void RenketuSyori(List<HashSet<int>> pUnionSetList, int p1, int p2)
    {
        int wkInd1 = pUnionSetList.FindIndex(X => X.Contains(p1));
        int wkInd2 = pUnionSetList.FindIndex(X => X.Contains(p2));

        //UnionFind木に両方とも存在しない場合
        if (wkInd1 < 0 && wkInd2 < 0) {
            pUnionSetList.Add(new HashSet<int>() { p1, p2 });
        }
        //UnionFind木にp2のみが存在する場合
        else if (wkInd1 < 0 && wkInd2 >= 0) {
            pUnionSetList[wkInd2].Add(p1);
        }
        //UnionFind木にp1のみが存在する場合
        else if (wkInd1 >= 0 && wkInd2 < 0) {
            pUnionSetList[wkInd1].Add(p2);
        }
        //別々のUnionFind木なら木をマージ
        else if (wkInd1 != wkInd2) {
            pUnionSetList[wkInd1].UnionWith(pUnionSetList[wkInd2]);
            pUnionSetList.RemoveAt(wkInd2);
        }
    }
}