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: Wrong Answer)

const merge = (f1, f2) => {
    if (f1 && f2) {
        const s = new Set()
        for (const t of f1) {
            s.add(t)
        }
        for (const t of f2) {
            s.add(t)
        }
        return s
    }
    return f1 || f2 || (new Set())
}


const processData = (lines) => {
    const [n, m] = lines[0].split(' ').map( x => +x)
    let friendships = {}
    let uniqueMap = {}
    for (let i=0; i<m; i++) {
        const f = lines[i+1].split(' ').map(x => +x)
        let friendItem = merge(friendships[f[0]], friendships[f[1]])
        friendships[f[0]] = friendItem
        friendships[f[1]] = friendItem
        friendItem.add(f[0])
        friendItem.add(f[1])
    }

    let maxCount = 1
    for (let p in friendships) {
        maxCount = Math.max(maxCount, friendships[p].size)
    }

    console.log(maxCount)
}

let i = ''
process.stdin.on('data', c => i += c)
process.stdin.on('end', () => {
    const {EOL} = require('os')
    const lines = i.split(EOL) /*your input text, split by lines*/
    processData(lines)
})