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.io.IOException
import java.lang.NumberFormatException
import java.lang.StringBuilder
import java.util.ArrayDeque
import kotlin.math.max
import kotlin.math.min

object DMain{
    fun solve() {
        val n = nextInt()
        val m = nextInt()

        val par = IntArray(n)
        val rank = IntArray(n)
        for(i in par.indices){
            par[i] = i
            rank[i] = 0
        }

        for (i in 1..m){
            val a = nextInt() - 1
            val b = nextInt() - 1
            unite(par, rank, a, b)
        }

        val num = IntArray(n){0}
        par.forEach { num[it]++ }
        println(num.max())

    }

    fun find(par: IntArray, rank: IntArray, x: Int): Int{
        if(par[x] == x){
            return x
        }else{
            par[x] = find(par, rank, par[x])
            return par[x]
        }
    }

    fun unite(par: IntArray, rank: IntArray, x: Int, y: Int){
        val mx = find(par, rank, x)
        val my = find(par, rank, y)
        if(mx == my) return

        if(rank[mx] < rank[my]){
            par[mx] = my
        }else{
            par[my] = mx
            if(rank[mx] == rank[my]) rank[mx]++
        }
    }

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




        // Scanner based on uwi-san's Java code
    val stream = System.`in`
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0

    fun hasNextByte(): Boolean{
        if(ptr < buflen){
            return true
        }else{
            ptr = 0
            try{
                buflen = stream.read(buffer)
            }catch (e: IOException){
                e.printStackTrace()
            }
            if(buflen <= 0){
                return false
            }
        }
        return true
    }

    fun readByte() =
            if(hasNextByte()) buffer[ptr++]
            else -1

    fun isPrintableChar(c: Byte) = c in 33..126

    fun hasNext(): Boolean{
        while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++
        return hasNextByte()
    }

    fun next(): String{
        if(!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while(isPrintableChar(b)){
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun nextLong(): Long{
        if(!hasNext()) throw NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if(b == '-'.toByte()){
            minus = true
            b = readByte()
        }
        if(b !in '0'.toByte()..'9'.toByte())
            throw NumberFormatException()
        while(true){
            if(b in '0'.toByte()..'9'.toByte()){
                n *= 10
                n += b - '0'.toByte()
            }else if(!isPrintableChar(b)){
                return if(minus) -n else n
            }else{
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextInt(): Int{
        val n1 = nextLong()
        if(n1 !in Int.MIN_VALUE..Int.MAX_VALUE)
            throw NumberFormatException()
        return n1.toInt()
    }

    fun NextDouble() = next().toDouble()
}

fun main(){
    DMain.solve()
}