Longest path

Given a directed acyclic graph, the task is to find the longest path in it.

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 $(n\le 10000,m\le 100000)$. The next $m$ lines contain descriptions of the arcs, one per line. Arc number $i$ is described by two natural numbers $b_i$ and $e_i$ - the start and end of the arc, respectively $(1\le b_i,e_i\le n)$.

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