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D - Friends

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.

5 3
1 2
3 4
5 1

3

Dividing them into three groups such as $\{1,3\}$, $\{2,4\}$, and $\{5\}$ achieves the goal.

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

4

10 4
3 1
4 1
5 9
2 6

3