Score : $400$ points
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?
Input is given from Standard Input in the following format:
$N$ $M$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$
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