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: