P9079 [PA 2018] Heros

**This problem is translated from [PA 2018](https://sio2.mimuw.edu.pl/c/pa-2018-1/dashboard/) Round 2 [Heros](https://sio2.mimuw.edu.pl/c/pa-2018-1/p/her/).** Given a directed acyclic graph with $n$ nodes and $m$ directed edges. You need to delete $k$ nodes and all edges incident to them, so that the length of the longest path in the graph is as small as possible.

The first line contains three integers $n$, $m$, and $k$. The next $m$ lines each contain two integers $x$ and $y$, indicating that there is a directed edge from node $x$ to node $y$.

Output one integer in one line, the minimum possible length of the longest path in the graph.

#### Explanation for Sample 1 After deleting node $4$, the length of the longest path in the graph is $2$. This is the minimum value we can achieve. You can verify that among all possible choices, the minimum possible longest-path length is $2$.  ------------ #### Constraints **This problem uses bundled testdata.** For $100\%$ of the testdata: - $1 \le n \le 300$ - $0 \le m \le 400$ - $0 \le k \le \min(n,4)$ - $1 \le x < y \le n$ Translated by ChatGPT 5