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.util.*
import kotlin.math.max

fun main() {
    val (n, m) = readInts()

    val neighbors = Array<MutableSet<Int>>(n + 1) { mutableSetOf() }

    repeat(m) {
        val (a, b) = readInts()
        if (b !in neighbors[a]) {
            neighbors[a].add(b)
            neighbors[b].add(a)
        }
    }

    val seen = BooleanArray(n + 1)

    fun bfs(v: Int): Int {
        val queue = LinkedList<Int>()
        queue.add(v)
        seen[v] = true
        var size = 0
        while (queue.isNotEmpty()) {
            val curr = queue.removeFirst()
            size++
            for (u in neighbors[curr]) {
                if (!seen[u]) {
                    seen[u] = true
                    queue.add(u)
                }
            }
        }
        return size
    }

    var ans = 0

    for (i in 1..n) {
        if (neighbors[i].isNotEmpty() && !seen[i]) {
            ans = max(bfs(i), ans)
        }
    }

    println(ans)
}

// Input Reader
private fun readLn() = readLine()!!

private fun readStrings() = readLn().trim().split(" ")
private fun readInts() = readStrings().map { it.toInt() }