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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
	"math"
)

func unUsedFunction() string {
	return "I am unused unexported function"
}
func UnUsedFunction() string {
	return "I am unused exported function"
}
func swap(a int, b int) (int, int) {
	return b, a
}
func (u UnionFind) Size(x int) int {
	return -u.par[u.Find(x)]
}
func (u UnionFind) Same(x, y int) bool {
	return u.Find(x) == u.Find(y)
}
func (u UnionFind) Union(x, y int) {
	xr := u.Find(x)
	yr := u.Find(y)
	if xr == yr {
		return
	}
	if u.Size(yr) < u.Size(xr) {
		yr, xr = swap(yr, xr)
	}
	u.par[yr] += u.par[xr]
	u.par[xr] = yr
}
func (u UnionFind) Find(x int) int {
	if u.par[x] < 0 {
		return x
	}
	u.par[x] = u.Find(u.par[x])
	return u.par[x]
}
func NewUnionFind(N int) *UnionFind {
	u := new(UnionFind)
	u.par = make([]int, N)
	for i := range u.par {
		u.par[i] = -1
	}
	return u
}

type UnionFind struct{ par []int }

func ModPow() int64 {
	return int64(math.Max(1, 3))
}
func main() {
	var n, m int
	fmt.Scan(&n, &m)
	uf := NewUnionFind(n)
	for i := 0; i < m; i++ {
		var a, b int
		fmt.Scan(&a, &b)
		a--
		b--
		uf.Union(a, b)
	}
	ans := 0
	for i := 0; i < n; i++ {
		if ans < uf.Size(i) {
			ans = uf.Size(i)
		}
	}
	fmt.Println(ans)
}