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 PyPy3 (7.3.0) (judge verdict: Accepted)

from sys import stdin
readline = stdin.readline
def r_map(): return map(int, readline().rstrip().split())

class UnionFind:
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * (n + 1)
        self.rank = [0] * (n + 1)
        self.max_size = 1

    def root(self, x):
        if(self.parents[x] < 0):
            return x
        else:
            self.parents[x] = self.root(self.parents[x])
            return self.parents[x]

    def unite(self, x, y) -> bool:
        x = self.root(x)
        y = self.root(y)
        if x == y:
            return False
        if self.rank[x] > self.rank[y]:
            self.parents[x] += self.parents[y]
            self.parents[y] = x
        else:
            self.parents[y] += self.parents[x]
            self.parents[x] = y
            if self.rank[x] == self.rank[y]:
                self.rank[y] += 1
        self.max_size = max(self.max_size, self.size(x))
        return True

    def members(self, x):
        root = self.root(x)
        return [i for i in range(self.n) if self.root(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def is_same(self, x, y) -> bool:
        return self.root(x) == self.root(y)

    def size(self, x):
        return -self.parents[self.root(x)]

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}


def main():
    N, M = r_map()
    uf = UnionFind(N)
    for _ in range(M):
        a, b = r_map()
        uf.unite(a, b)
    print(uf.max_size)

if __name__ == "__main__":
    main()