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: Runtime Error)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdbool.h>
typedef long long ll;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define REP(i,l,r) for(ll i=l; i<(ll)(r); i++)
#define max(l,r) ((l)>(r)?l:r)
#define min(l,r) ((l)<(r)?l:r)
#define swap(l,r) {ll tp=l;l=r;r=tp;}
const ll MOD = 1000000007;

/////Union Find/////
int par[1010101];   //par:-1*(size of set), chi:par
void UF(int n) {
    for (int i = 0; i < n; i++){
        par[i] = -1;
    }
}
int root(int x) {
    if (par[x] == x) return x;
    return par[x] = root(par[x]);
}
void unite(int x, int y) {
    int rx = root(x);
    int ry = root(y);
    if (rx == ry) return;
    if(par[rx] > par[ry]) swap(rx,ry);
    par[rx] += par[ry];
    par[ry] = rx;
}
int same(int x, int y) {
    return (root(x) == root(y)?1:0);
}
int size(int x) {
    return (-par[root(x)]);
}
/////----------/////

int main() {
    int n, m, flag = 0;
    scanf("%d%d", &n, &m);
    UF(n);
    rep(i,m){
        int a, b;
        scanf("%d%d", &a, &b);
        a--; b--;
        if(!same(a,b)) unite(a,b);
    }
    int ans = 1;
    rep(i,n){
        ans = max(size(i),ans);
    }

    printf("%d\n",ans);
}