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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN,"%d%d",$n,$m);
$p = array();
$size = array();
for($i=1;$i<=$n;$i++) $p[$i] = $i;
//for($i=1;$i<=$n;$i++) $size[$i] = 1;
array_fill(1,$n,1);

function root($x){
  global $p;
  if($x==$p[$x]){
    return $x;
  }
  return root($p[$x]);
}
function unite($a,$b){
  global $p;
  global $size;
  if($b>$a){
    $tmp = $a;
    $a = $b;
    $b = $tmp;
  }
  $b_root = root($b);
  $a_root = root($a);
  $p[$b_root] = $a_root; 
  $size[$a_root] += $size[$b_root];
}

for($i=0;$i<$m;$i++){
	fscanf(STDIN,"%d%d",$a,$b);
	unite($a,$b);
}

rsort($size);
echo $size[0];