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.Text;
using System.Collections.Generic;
class abc049_d {
    static int __cnt = 0;
    static string __mark = "###";
    static void Main(string[] args) {
#if LOCAL_ENVIRONMENT
        StreamReader __sr = new StreamReader("stdin.txt");
        string __str = __sr.ReadToEnd();
        __sr.Close();
        int __index = __str.IndexOf(__mark, 0);
        while (__index != -1) {
            __index = __str.IndexOf(__mark, __index + __mark.Length);
            __cnt++;
        }
        if (__cnt > 0) {
            Console.Write("Eenter test data no(1-{0})? ", __cnt);
            Console.Out.Flush();
            if (!int.TryParse(Console.ReadLine(), out __cnt)) __cnt = 1;
            Console.WriteLine("Select/Default test data: {0}", __cnt);
        }
        var stdin = new System.IO.StreamReader("stdin.txt");
        Console.SetIn(stdin);
#endif
        SimpleScanner sc = new SimpleScanner(__cnt);
        int N = sc.NextInt(), K = sc.NextInt(), L = sc.NextInt();
#if LOCAL_ENVIRONMENT
    Console.Error.WriteLine($"N:{N}, K:{K}, L:{L}");
#endif
        var U1 = new UnionFind(N);
        for (var m = 0; m < K; m++) {
            int p = sc.NextInt() - 1, q = sc.NextInt() - 1;
#if LOCAL_ENVIRONMENT
    Console.Error.WriteLine($"p:{p}, q:{q}");
#endif
            U1.unite(p, q);
        }
        var U2 = new UnionFind(N);
        for (var m = 0; m < L; m++) {
            int r = sc.NextInt() - 1, s = sc.NextInt() - 1;
#if LOCAL_ENVIRONMENT
    Console.Error.WriteLine($"r:{r}, s:{s}");
#endif
            U2.unite(r, s);
        }
#if LOCAL_ENVIRONMENT
  Console.Error.WriteLine($"UnionFind_1: {U1.par.ToStringA()}");
  Console.Error.WriteLine($"UnionFind_2: {U2.par.ToStringA()}");
#endif

        var C = new Dictionary<Item, int>();
        for (var m = 0; m < N; m++) {
            var item = new Item(U1.root(m), U2.root(m));
            int n;
            if (C.ContainsKey(item)) n = C[item];
            else C.Add(item, n = 0);
            C[item] = ++n;
        }

        var ans = new StringBuilder();
        for (var m = 0; m < N; m++) {
            var item = new Item(U1.root(m), U2.root(m));
            int n;
            if (C.ContainsKey(item)) n = C[item];
            else n = 0;
            if (m > 0) ans.Append(" ");
            ans.Append(n.ToString());
        }
        Console.WriteLine(ans);
    } //Main

    public class Item: IEquatable<Item> {
        public int u1 { get; set; }
        public int u2 { get; set; }
        public Item(int u1, int u2) {
            this.u1 = u1;
            this.u2 = u2;
        }
        public bool Equals(Item other) {
            if (other == null) return false;
            return (this.u1 == other.u1 && this.u2 == other.u2);
        }
        public override bool Equals(Object obj) {
            if (obj == null) return false;
            Item other = obj as Item;
            return this.Equals(other);
        }
        public override int GetHashCode() {
            long u = this.u1 << 32 | this.u2;
            return u.GetHashCode();
        }
        public override string ToString() {
            return $"[u1:{this.u1}, u2:{this.u2}]";
        }
    }

    public class UnionFind {
        public int[] rank, par, size;
        public UnionFind(int n) {
            this.rank = new int[n];
            this.par = new int[n];
            this.size = new int[n];
            for (var i = 0; i < n; i++) {
                this.par[i] = i;
                this.size[i] = 1;
            }
        }
        public int find(int x) {
            if (this.par[x] == x) return x;
            return this.par[x] = this.find(this.par[x]);
        }
        public bool union(int x, int y) {
            var rx = this.root(x);
            var ry = this.root(y);
            if (rx == ry) return false;

            if (this.rank[rx] < this.rank[ry]) {
                int w = rx; rx = ry; ry = w; 
            } else if (this.rank[rx] == this.rank[ry]) {
                this.rank[rx] += 1;
            }
            this.par[ry] = rx;
            this.size[rx] += this.size[ry];
            return true;
        }
        public bool isSame(int x, int y) {
            return this.root(x) == this.root(y);
        }
        public int getSize(int x) {
            return this.size[this.find(x)];
        }
        public int root(int x) { return this.find(x); }
        public bool unite(int x, int y) { return this.union(x, y); }
    }

    public class SimpleScanner {
        private int cnt;
        private string[] items;
        public SimpleScanner(int cnt = 0) {
            this.cnt = 0;
            var sb = new StringBuilder();
            var s = Console.ReadLine();
            while (s != null) {
                sb.Append(s + " ");
                s = Console.ReadLine();
            }
            this.items = sb.ToString().Split(' ');
#if LOCAL_ENVIRONMENT
            if (cnt > 0) {
                int index = Array.IndexOf(this.items, __mark + cnt.ToString());
                this.cnt = index + 1;
            }
            Console.Error.WriteLine("SimpleScanner.cnt: {0}", this.cnt);
            Console.Error.WriteLine("SimpleScanner.items: {0}", this.items.ToStringA());
#endif
        }
        public void SetCnt(int n) { this.cnt = n; }
        public int NextInt() {
            return int.Parse(this.items[this.cnt++]);
        }
        public long NextLong() {
            return long.Parse(this.items[this.cnt++]);
        }
        public string NextString() {
            return this.items[this.cnt++];
        }
        public int[] NextIntArray(int n) {
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            var result = new int[n];
            for (var i = 0; i < n; i++) result[i] = this.NextInt();
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("{0}", result.ToStringA());
#endif
            return result;
        }
        public long[] NextLongArray(int n) {
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            var result = new long[n];
            for (var i = 0; i < n; i++) result[i] = this.NextLong();
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("{0}", result.ToStringA());
#endif
            return result;
        }
        public string[] NextStringArray(int n) {
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            var result = new string[n];
            for (var i = 0; i < n; i++) result[i] = this.NextString();
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("{0}", result.ToStringA());
#endif
            return result;
        }
        public int[][] NextInt2Col(int n) {
            const int M = 2;
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            int[][] result = new int[M][] {
                new int[n],
                new int[n],
            };
            for (var i = 0; i < n; i++) {
                result[0][i] = this.NextInt();
                result[1][i] = this.NextInt();
            }
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("NextInt2Col: [");
            for (var i = 0; i < M; i++)
                Console.Error.WriteLine("  {0},", result[i].ToStringA());
            Console.Error.WriteLine("]");
#endif
            return result;
        }
    }

}
static class Extensions {
    public static string ToStringA<T>(this T[] array, string separator = ", ", string braces = "[]") {
        string bL = braces.Length > 0 ? braces[0].ToString() : "";
        string bR = braces.Length > 1 ? braces[1].ToString() : "";
        return bL + String.Join(separator, array) + bR;
    }
}