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: Runtime Error)

import collections
N,M = map(int,input().split())
A = [list(map(int, input().split())) for i in range(M)]
visit = set()
G = collections.defaultdict(set)
for idx,(f,to) in enumerate(A):
    G[f].add(to)

cache = {}
    
def dfs(start):
    if start in cache:
        return cache[start]
    ma = 0
    for i in G[start]:
        if i not in visit:
            visit.add(i)
            ma = max(ma,dfs(i))
            visit.remove(i)
    cache[start] = ma + 1 
    return ma + 1

ma = 0 
for f,to in A:
    visit.add(f)
    ma = max(ma,dfs(f))
    visit.remove(f)
print(ma - 1)