There is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1,2,\dots ,N$, and for each $i$ $(1\le i\le M)$, 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.
• $2\le N\le {10}^5$
• $1\le M\le {10}^5$
• $1\le x_i,y_i\le N$
• All pairs $(x_i,y_i)$ are distinct.
• $G$ does not contain directed cycles.

Input Specification

The first line will contain 2 space separated integers $N,M$.

The next $M$ lines will contain 2 space separated integers, $x_i,y_i$.

Output Specification

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

Sample Input 1

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

Sample Output 1

3

Explanation For Sample 1

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

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

Explanation For Sample 2

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

Sample Input 3

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

Sample Output 3

3

Explanation For Sample 3

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