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 Python (3.8.2) (judge verdict: Accepted)

class uft():
    def __init__(self,n):
        #pは代表元か-1
        self.p=[ -1 for i in range(n)]
        #ランク　木の深さ
        self.r=[ 1 for i in range(n)]
        #要素数
        self.e=[ 1 for i in range(n)]
        
    def find(self,x):
        if(self.p[x]==-1):
            return x
        else:
            self.p[x]=self.find(self.p[x])
            return self.find(self.p[x])
        
    def unite(self,x,y):
        x=self.find(x)
        y=self.find(y)
        if(x==y):
            return
        
        if(self.r[x]>self.r[y]):
            tmp=x
            x=y
            y=tmp
        
        if(self.r[x]==self.r[y]):
            self.r[y]+=1
        
        self.e[y]+=self.e[x]
            
        if(x!=y):
            self.p[x]=y
        return
    
    def tsize(self,x):
        return self.e[self.find(x)]
n,m=map(int,input().split())

uf=uft(n)
for i in range(m):
    x,y=map(int,input().split())
    x-=1
    y-=1
    uf.unite(x,y)
ans=0
for i in range(n):
    ans=max(ans,uf.tsize(i))
print(ans)