101773: [AtCoder]ABC177 D - Friends
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
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