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