Problem:
Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3

Solution in Kotlin (1.3.71) (judge verdict: Runtime Error)

import kotlin.String
import kotlin.math.max

fun main(args: Array<String>) {
    val (n, m) = readIntList()
    val fs = mutableListOf<MutableSet<Int>>()

    var uf = UnionFind(n)
    repeat(m) {
        val (a, b) = readIntList().map { it - 1 }
        uf.unite(a, b)
    }

    var ans = 0
    for (i in 0 until n) {
        ans = max(ans, uf.size(i))
    }
    println(ans)
}

// read
fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)

fun MutableList<Int>.swap(x: Int, y: Int) {
    val tmp = this[x]
    this[x] = this[y]
    this[y] = tmp
}

class UnionFind(size: Int) {
    private val r: MutableList<Int> = MutableList(size) { -1 }

    fun root(x: Int): Int {
        if (r[x] < 0) return x
        r[x] = root(r[x])
        return r[x]
    }

    fun unite(x: Int, y: Int): Boolean {
        val x = root(x)
        val y = root(y)
        if (x == y) return false
        if (r[x] > r[y]) r.swap(x, y)
        r[x] += r[y]
        r[y] = x
        return true
    }

    fun size(x: Int): Int = -r[root(x)]
}