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: Time Limit Exceeded)


import java.util.*
import kotlin.collections.HashSet


fun main() {

    val (N, M) = readInts()

    val set = HashSet<Int>(N)

    for (i in 1..N) {
        set.add(i)
    }
    val arr = arrayOfNulls<HashSet<Int>>(N + 1)

    repeat(M) {
        val (a, b) = readInts()

        if (arr[a] == null) {
            arr[a] = HashSet()
        }

        arr[a]!!.add(b)

        if (arr[b] == null) {
            arr[b] = HashSet()
        }
        arr[b]!!.add(a)
    }

    var groupSize = 0
    while (set.isEmpty().not()) {
        val newSize = bfs(arr, set)
        if (newSize > groupSize) {
            groupSize += newSize - groupSize
        }
    }
    println(groupSize)
}

private fun bfs(arr: Array<HashSet<Int>?>, set: HashSet<Int>): Int {
    val queue: Queue<Int> = LinkedList()

//    println("before bfs set $set")
    queue.add(set.first())
    var groupSize = 0
    while (queue.isEmpty().not()) {
        val top = queue.remove()
        if (set.isEmpty()) break
        if (set.contains(top).not()) continue
        
        set.remove(top)
        groupSize++
        val child = arr[top]

        child?.forEach {
            if (set.contains(it)) {
                queue.add(it)
            }
        }
    }
//    println("set is $set groupSize $groupSize")
    return groupSize
}

private fun readLn() = readLine()!! // string line
private fun readInt() = readLn().toInt() // single int
private fun readStrings() = readLn().split(" ") // list of strings
private fun readInts() = readStrings().map { it.toInt() } // list of ints