There is a directed graph $G$ with $n$ vertices and $m$ edges. The vertices are numbered $1, 2, ..., n$, and for each $i\:(1 \le i \le m)$, the $i$-th directed edge goes from vertex $x_i$ to vertex $y_i$. $G\:$ does not contain directed cycles. Find the length of the longest directed path in $G$. Here, the length of a directed path is the number of edges in it. \InputFile The first line contains two integers: number of vertices $n\:(2 \le n \le 10^5)$ and number of edges $m\:(1 \le m \le 10^5)$. Each of the next $m$ lines contains two integer $x_i, y_i\:(1 \le x_i, y_i \le n)$ that describe the edge of the graph. \OutputFile Print the length of the longest directed path in $G$. \includegraphics{https://static.eolymp.com/content/lr/lrppgvrc194v5amr0dfe6kjaio.gif}