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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

function Main(input) {
  const lines = input.split('\n');
  const [N, M] = lines[0].split(' ').map(i => parseInt(i));
  const R = lines.splice(1, M).map(r => r.split(' ').map(v => parseInt(v) - 1));
  const relmat = new Array(N).fill(0).map(_ => new Set());
  const done = new Array(N).fill(false);
  R.forEach(r => {
    l = r[0];
    r = r[1];
    relmat[l].add(r);
    relmat[r].add(l)
  });
  let queue = [];
  let max = 0;
  while (true) {
    if (done.indexOf(false) === -1) {
      break;
    } else {
      queue.push(done.indexOf(false));
    }
    let num = 0;
    while (queue.length !== 0) {
      const next = queue.shift();
      if (done[next] === false) {
        done[next] = true;
        num = num + 1;
        queue = queue.concat([...relmat[next]].filter(c => done[c] === false));
      }
    }
    if (num > max) max = num;
  }
  console.log(max);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));