Problem:
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.

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:

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import deque
n, m = map(int, input().split( ))
Edg = [[] for _ in range(n)]
#rev_Edg =  [[] for _ in range(n)]

Visited = [0]*n
Root_check = [1]*n
Dist = [0]*n
for i in range(m):
    v1,v2 = map(int, input().split( ))
    v1-=1
    v2-=1
    Edg[v1].append(v2)
    Root_check[v2] = 0
    
Roots = []
for i in range(n):
    if Root_check[i] == 1:
        Roots.append(i)
Q = deque()
for r in Roots:
    Q.append(r)
    while len(Q) > 0:
        v = Q.popleft()
        for w in Edg[v]:
            Dist[w] = Dist[v] +1
            Q.append(w)

print(max(Dist))