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 C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

#define KI_MAX 212345

int ki[KI_MAX];

void ki_init(void) {
	int i;
	for (i = 0; i < KI_MAX; i++) {
		ki[i] = 1;
	}
}

int ki_root(int x) {
	if (ki[x] > 0) {
		return x;
	} else {
		int root = ki_root(-ki[x]);
		ki[x] = -root;
		return root;
	}
}

int ki_size(int x) {
	return ki[ki_root(x)];
}

void ki_merge(int a, int b) {
	int ar = ki_root(a);
	int br = ki_root(b);
	if (ar != br) {
		int as = ki_size(ar);
		int bs = ki_size(br);
		if (as >= bs) {
			ki[ar] += ki[br];
			ki[br] = -ar;
		} else {
			ki[br] += ki[ar];
			ki[ar] = -br;
		}
	}
}

int main(void) {
	int N, M;
	int i;
	int kotae = 0;
	if (scanf("%d%d", &N, &M) != 2) return 1;
	ki_init();
	for (i = 0; i < M; i++) {
		int A, B;
		if (scanf("%d%d", &A, &B) != 2) return 1;
		ki_merge(A, B);
	}
	for (i = 1; i <= N; i++) {
		int num = ki_size(i);
		if (num > kotae) kotae = num;
	}
	printf("%d\n", kotae);
	return 0;
}