Problem Description

Iruka has $ N $ types of drugs numbered from $ 1 $ to $ N $.
She also has a list detailing the handling of these drugs.
This list contains $ M $ entries, and the $ i $th entry (1 ≤ i ≤ M) states that "mixing drugs numbered $ a_i $ and $ b_i $ will produce poison."

Iruka wants to mix as many types of drugs as possible without producing poison based on the list.
What is the maximum number of drug types she can mix?

Input Format

The input is given from the standard input in the following format:

$ N $ $ M $ $ a_1 $ $ b_1 $ $ : $ $ a_M $ $ b_M $

Output Format

Output the maximum number of drug types Iruka can mix.

Sample Input and Output

Sample Input #1

4 1
1 2

Sample Output #1

3

Sample Input #2

1 0

Sample Output #2

1

Sample Input #3

20 16
1 8
1 16
2 19
3 5
3 10
5 7
5 13
6 9
7 8
7 11
7 14
7 15
8 12
9 12
9 17
15 20

Sample Output #3

12

Notes/Hints

Constraints

• $ 1 ≤ N ≤ 40 $
• $ 0 ≤ M ≤ N(N-1)/2 $
• $ 1 ≤ a_i < b_i ≤ N $
• $ a_i ≠ a_j $ or $ b_i ≠ b_j $ (1 ≤ i < j ≤ M)
• All inputs are integers.

Sample Explanation 1

Mixing drugs numbered $ 1 $ and $ 2 $ will produce poison, so all drugs cannot be mixed. On the other hand, mixing drugs numbered $ 1 $, $ 3 $, and $ 4 $ will not produce poison. Therefore, the maximum number of drug types that can be used is $ 3 $, so output $ 3 $.

见题面 Input 部分

见题面 Output 部分