Longest path — Eolymp

Input

The first line of the input file contains two natural numbers $n$ and $m$ — the number of vertices and arcs in the graph, respectively $(n \leq 10000, m \leq 100000)$ (n \leq 10000,\ m \leq 100000). The next $m$ lines contain descriptions of the arcs, one per line. Arc number $i$ is described by two natural numbers $b_{i}$ b_i and $e_{i}$ e_i — the start and end of the arc, respectively $(1 \leq b_{i}, e_{i} \leq n)$ (1 \leq b_i,\ e_i \leq n).

The input graph contains no cycles or loops.

Output

The first line of the output file should contain a single natural number — the number of arcs in the longest path.

Examples

Example 1

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