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: Accepted)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.io.PrintWriter
import kotlin.math.max

val br = BufferedReader(InputStreamReader(System.`in`))
val out = PrintWriter(System.out)

fun readInteger() = Integer.parseInt(br.readLine())
fun readLong() = java.lang.Long.parseLong(br.readLine())
fun readStringList() = br.readLine()!!.split(' ')
fun readIntegerList() = readStringList().map(Integer::parseInt)
fun readLongList() = readStringList().map(java.lang.Long::parseLong)
fun readDoubleList() = readStringList().map(java.lang.Double::parseDouble)


class UnionFind(n: Int) {
    private val rank = IntArray(n) { 0 }
    private val parent = IntArray(n) { -1 }

    fun find(x: Int): Int {
        if (parent[x] < 0) {
            return x
        }
        parent[x] = find(parent[x])
        return parent[x]
    }

    fun unite(x: Int, y: Int) {
        val x1 = find(x)
        val y1 = find(y)
        if (x1 == y1) {
            return
        }
        if (rank[x1] < rank[y1]) {
            parent[y1] += parent[x1]
            parent[x1] = y1
        } else {
            parent[x1] += parent[y1]
            parent[y1] = x1
            if (rank[x1] == rank[y1]) {
                rank[x1]++
            }
        }
    }

    fun same(x: Int, y: Int): Boolean {
        return find(x) == find(y)
    }

    fun size(x: Int): Int {
        return -parent[find(x)]
    }
}
fun main() {
    val (n, m) = readIntegerList()
    val abs = mutableListOf<List<Int>>()
    val union = UnionFind(n)
    for (i in 0 until m) {
        val (a,b)=readIntegerList()
        union.unite(a-1,b-1)
    }
    var ans=0
     for (i in 0 until n) {
        ans=max(ans,union.size(i))
    }
    println(ans)


}