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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*
import kotlin.*

import java.io.InputStream
import java.lang.NumberFormatException
import java.lang.StringBuilder


fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = FastScanner()
        val n = sc.nextInt()
        val k = sc.nextInt()
        val l = sc.nextInt()

        val pq = Array(k) { sc.nextInt() - 1 to sc.nextInt() - 1 }
        val lr = Array(l) { sc.nextInt() - 1 to sc.nextInt() - 1 }

        // 道路でつながっているか
        val uf1 = UnionFind(n)
        pq.forEach {
            uf1.unite(it.first, it.second)
        }

        // 鉄道で繋がっているか
        val uf2 = UnionFind(n)
        lr.forEach {
            uf2.unite(it.first, it.second)
        }

        val map = mutableMapOf<Pair<Int, Int>, Int>()

        for (i in 0 until n) {
            val p = uf1.find(i) to uf2.find(i)
            map[p] = (map[p] ?: 0) + 1
        }

        println((0 until n).map {
            val p = uf1.find(it) to uf2.find(it)
            map[p]
        }.joinToString(" "))
    }
}

class UnionFind(private val v: Int) {
    // 頂点iの親 par[i] == iなら iは根
    private val par = Array(v) { it }
    // iを根とする部分木のサイズ
    private val size = Array(v) { 1 }

    // iが含まれる木の根
    fun find(i: Int): Int = if (par[i] == i) i else find(par[i])

    // xとyが同じグループに含まれるか?
    fun same(x: Int, y: Int) = find(x) == find(y)

    // iが含まれるグループのサイズ
    fun getSize(i: Int) = size[find(i)]

    // xとyを繋げる 元から同じグループならfalse
    fun unite(x: Int, y: Int): Boolean {
        val rootX = find(x)
        val rootY = find(y)

        if (rootX == rootY) return false

        // データ構造をマージする一般的なテク
        if (size[rootX] > size[rootY]) {
            par[rootY] = rootX
            size[rootX] += size[rootY]
        } else {
            par[rootX] = rootY
            size[rootY] += size[rootX]
        }

        return true
    }
}


class FastScanner {
    companion object {
        val input: InputStream = System.`in`
        val buffer = ByteArray(1024) { 0 }
        fun isPrintableChar(c: Int): Boolean = c in 33..126
    }

    var ptr = 0
    var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            buflen = input.read(buffer)
            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextDouble(): Double = next().toDouble()
}