P11073 Game King

You have traveled to the world of Yu-Gi-Oh!, and now you are dueling against your opponent—a directed graph with $n$ vertices and $m$ edges. Then I forgot what happened. A true duelist believes everything is inevitable. To deal with the duel in front of you, you need to know how many vertices $x$ satisfy the following condition. - For any vertex $y$, it holds that either $x$ can reach $y$ or $y$ can reach $x$ (we consider that a vertex can reach itself).

The first line contains two positive integers $n, m$, representing the number of vertices and the number of edges in the given directed graph. The next $m$ lines each contain two positive integers $x, y$, denoting a directed edge $x \to y$.

Output one integer in one line: the answer, i.e., how many vertices satisfy that every vertex can reach it or be reached from it.

### Explanation for Sample 1 It can be proven that only vertices $1$ and $4$ satisfy the requirement. Since vertex $3$ cannot reach vertex $2$ and also cannot be reached from vertex $2$, vertices $2$ and $3$ do not satisfy the requirement. ### Sample 2 See the attached files `gameh2.in` and `gameh2.ans`. The constraints of this sample are the same as test point $2$. ### Sample 3 See the attached files `gameh3.in` and `gameh3.ans`. The constraints of this sample are the same as test point $3$. ### Constraints This problem has $10$ test points. The test points are not evenly distributed, and the score for each test point is as follows. |Test Point ID|Score|$n=$|$m=$| |:-:|:-:|:-:|:-:| |$1\sim 2$|$5$|$10$|$20$| |$3\sim 4$|$5$|$100$|$10^3$| |$5\sim 6$|$5$|$10^3$|$10^4$| |$7\sim 8$|$15$|$5\times 10^4$|$5\times 10^5$| |$9\sim 10$|$20$|$10^6$|$3\times 10^6$| For all testdata, it is guaranteed that $10 \le n \le 10^6$ and $20 \le m \le 3\times 10^6$. For odd-numbered test points, it is guaranteed that the given graph has no cycles with **more than $1$ distinct vertex**. ### Hint **The input and output size of this problem is large, so please use fast I/O.** Translated by ChatGPT 5