Score : $100$ points

Problem Statement

There is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \ldots, N$, and for each $i$ ($1 \leq i \leq M$), the $i$-th directed edge goes from Vertex $x_i$ to $y_i$. $G$ 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.

Constraints

• All values in input are integers.
• $2 \leq N \leq 10^5$
• $1 \leq M \leq 10^5$
• $1 \leq x_i, y_i \leq N$
• All pairs $(x_i, y_i)$ are distinct.
• $G$ does not contain directed cycles.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$x_1$ $y_1$

$x_2$ $y_2$

$:$

$x_M$ $y_M$

Output

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

4 5
1 2
1 3
3 2
2 4
3 4

3

The red directed path in the following figure is the longest:

6 3
2 3
4 5
5 6

2

The red directed path in the following figure is the longest:

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

3

The red directed path in the following figure is one of the longest: