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 Julia (1.4.0) (judge verdict: Accepted)

function main()
    n,m=myreads(Int)

    # -----------Union-Find-----------
    par=Vector{Int}([i for i=1:n])
    siz=ones(Int,n)
    function root(x::Int)
        index=par[x]
        while par[index]!=index
            index=par[index]
        end
        return index
    end
    function unite(x::Int,y::Int)
        rx,ry=root(x),root(y)
        if rx==ry
            return 0
        elseif rx>ry
            rx,ry=ry,rx
        end
        par[ry]=rx
        siz[rx]+=siz[ry]
    end
    function same(x::Int,y::Int)
        isequal(root(x),root(y))
    end
    # --------------------------------

    for i=1:m
        a,b=myreads(Int)
        unite(a,b)
    end
    println(maximum(siz))
end

# ----------input function----------
sread()=chomp(readline())
sreads(sp=" ")=split(readline(),sp)
myread(ty)=parse(ty,sread())
myreads(ty)=parse.(ty,sreads())
main()