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: Accepted)

import sys

sys.setrecursionlimit(10**9)

n , m = map(int,input().split())

g = [[] for i in range(n)]

dp = [-1] *n
for _ in range(m):
  v1 , v2 = map(int,input().split())
  v1 -=1; v2 -=1
  g[v1].append(v2)
  
# finding longest path for vertice i
def dfs(i):
  if dp[i]!=-1:
    return dp[i]
  temp = 0
  for nv in g[i]:
    temp = max(temp, dfs(nv)+1)
  
  dp[i]=temp
  return temp
  
# finding overall longest path  
res = 0  
for i in range(n):
  res = max(res, dfs(i))
  
print(res)