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)

#!/usr/bin/env python3
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")
import sys,collections

N,M = map(int,sys.stdin.readline().split())
ab = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(M)) # multi line with multi param

parents = list(range(N))
def find(x):
  while parents[x] != x:
    x = parents[x]
    parents[x] = parents[parents[x]]
  return x
def union(s,t):
  sp = find(s)
  tp = find(t)
  if sp == tp:
    pass
  elif sp < tp:
    parents[sp] = tp
  else:
    parents[tp] = sp

for a,b in ab:
    union(a-1,b-1)
import collections
d = collections.defaultdict(int)
m = 0
for i in range(N):
    x = find(i)
    d[x] += 1
    m = max(m,d[x])
print(m)