Contest Duration: - (local time) (100 minutes) Back to Home
D - Friends /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

1 から 人 N までの N 人の人がいます。

「人 A_i と人 B_i は友達である」という情報が M 個与えられます。同じ情報が複数回与えられることもあります。

XY が友達、かつ、YZ が友達ならば、XZ も友達です。また、M 個の情報から導くことができない友達関係は存在しません。

### 制約

• 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

### 入力

N M
A_1 B_1
\vdots
A_M B_M


### 入力例 1

5 3
1 2
3 4
5 1


### 出力例 1

3


### 入力例 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4


### 出力例 2

4


### 入力例 3

10 4
3 1
4 1
5 9
2 6


### 出力例 3

3


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


### 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