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.

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.

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.

Sample Input 1

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

Sample Output 1

3

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

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

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

见题面 Input 部分

见题面 Output 部分