Longest Path

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.

Input

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.

Output

Print the length of the longest directed path in $G$.

Examples