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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;
using System.Globalization;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;

class Program
{
    static void Main()
    {
        var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
        SetOut(sw);
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";

    int N, K, L;
    void solve()
    {
        N = cin.nextint;
        K = cin.nextint;
        L = cin.nextint;

        var G = new HashSet<int>[N];
        for (int i = 0; i < N; i++)
        {
            G[i] = new HashSet<int>();
        }
        
        var UF1 = new UnionFind(N);
        for (int i = 0; i < K; i++)
        {
            UF1.Unite(cin.nextint - 1, cin.nextint - 1);
        }


        var A = Enumerable.Repeat(1, N).ToArray();

      
        for (int i = 0; i < L; i++)
        {
            int t = cin.nextint - 1;
            int s = cin.nextint - 1;

            if(UF1.Same(t,s))
            {
                var d = UF1.Weight(t);
                A[t] = d;
                A[s] = d;
            }
        }


        /*
        for (int i = 0; i < N - 1; i++)
        {
            for (int j = i + 1; j < N; j++)
            {
                if(UF1.Same(i,j) && UF2.Same(i,j))
                {
                    A[i]++;
                    A[j]++;
                }
            }
        }*/
        WriteLine(string.Join(" ", A));
    }

}

class UnionFind
{
    internal int[] rank;
    internal int[] p;
    internal int[] weight;
    public UnionFind(int size)
    {
        rank = new int[size];
        p = new int[size];
        weight = new int[size];
        for (int i = 0; i < size; i++)
        {
            rank[i] = 0;
            p[i] = i;
            weight[i] = 1;
        }
    }
    public void Unite(int x, int y)
    {
        x = FindSet(x);
        y = FindSet(y);
        if (x == y) return;
        if (rank[x] > rank[y])
        {
            p[y] = x;
            weight[x] += weight[y];
        }

        if (rank[x] < rank[y])
        {
            p[x] = y;
            weight[y] += weight[x];
        }
        if (rank[x] == rank[y])
        {
            p[x] = y;
            rank[y]++;
            weight[y] += weight[x];
        }
    }
    public bool Same(int x, int y)
    {
        return FindSet(x) == FindSet(y);
    }
    public int FindSet(int x)
    {
        var H = new HashSet<int>();
        while (p[x] != x)
        {
            H.Add(x);
            x = p[x];
        }
        foreach (var h in H)
        {
            p[h] = x;
        }
        return x;
    }
    public int Weight(int x)
    {
        return weight[FindSet(x)];
    }
}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}