Popular Cows

Problem Source

HAOI 2006

Problem Description

Every cow's dream is to become the most popular cow.

Now there are $N$ cows. You are given $M$ pairs of integers $(A, B)$, meaning cow $A$ thinks cow $B$ is popular. This relation is transitive: if $A$ thinks $B$ is popular and $B$ thinks $C$ is popular, then $A$ also thinks $C$ is popular. Your task is to find out how many cows are considered popular by all the cows.

Input Format

The first line contains two integers $N, M$ ($1 \leq N \leq 10^4,\ 0 \leq M \leq 5 \times 10^4$). The next $M$ lines each contain two integers $A, B$, meaning $A$ thinks $B$ is popular. (The information may be repeated, i.e. the same pair $(A, B)$ may appear multiple times.)

Output Format

Output one number: how many cows are considered popular by all the cows.

Sample Input

3 3
1 2
2 1
2 3

Sample Output

1

Constraints

• $1 \leq N \leq 10^4$
• $0 \leq M \leq 5 \times 10^4$