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 Ruby (2.7.1) (judge verdict: Wrong Answer)

N, M = gets.split.map(&:to_i)
A = Array.new M
B = Array.new M
groups = []
members = Array.new N + 1
group_alias = {}
result = 1
M.times do |m|
    _a, _b = gets.split.map(&:to_i)
    a, b = nil
    if _a < _b
        a = _a
        b = _b
    else
        a = _b
        b = _a
    end
    # warn "---"
    # warn [a, b].inspect
    if !members[a] && !members[b]
        groups.push({count: 2 })
        members[a] = members[b] = (groups.length - 1)
        if result == 1
            result = 2
        end
    elsif members[a] && members[b]
        unless members[a] == members[b]
            agroup = members[a]
            bgroup = members[b]
            if groups[agroup] == groups[bgroup]
                next
            end

            groups[agroup][:count] += groups[bgroup][:count]
            # groups[agroup][:members] += groups[bgroup][:members]
            groups[bgroup] = groups[agroup]
            if groups[agroup][:count] > result
                result = groups[agroup][:count]
            end
        end
    else
        g = members[a] || members[b]
        groups[g][:count] += 1
        unless members[a]
            members[a] = g
        end
        unless members[b]
            members[b] = g
        end
        if groups[g][:count] > result
            result = groups[g][:count]
        end
    end
    # warn members.inspect
    # warn groups.inspect
end

# warn groups.inspect
puts result