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: Wrong Answer)

import java.lang.IllegalArgumentException

fun main(args: Array<String>) {
	val (n, m) = readLine()?.split(" ")?.map {it.toInt()} ?: throw IllegalArgumentException()
	val unionFind = UnionFind(n)
	for (i in 0 until m) {
		unionFind.addUnion(readLine()?.split(" ")?.map {it.toInt()} ?: throw IllegalArgumentException())
	}
	println(unionFind.maxUnionSize())
}

data class UnionFind(val n: Int, val rootList: MutableList<Int> = MutableList(n+1) {it}) {
	fun addUnion(friends: List<Int>) {
		val (parent, child) = if (friends[0] < friends[1]) Pair(friends[0], friends[1]) else Pair(friends[1], friends[0])
		rootList[child] = rootList[parent]
	}
	fun maxUnionSize(): Int {
		var max = 0
		for (i in 1 until rootList.size) {
			if (max < rootList.count {it == i}) max = rootList.count {it == i}
			if (max > rootList.size - i + 1) break
		}
		return max
	}
}