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)

def path(start):
    if dp[start]!=-1:
        return dp[start]
    visited[start]=1
    maxi=-1
    for i in adjacency_list[start]:
        maxi=max(maxi,path(i))
    dp[start]=maxi+1
    return dp[start]
N,M=map(int,input().split())
dp=[-1]*(N+1)
visited=[0]*(N+1)
adjacency_list=[]
for i in range(N+1):
    adjacency_list.append([])
# print(adjacency_list)
for r in range(M):
    u,v=map(int,input().split())
    adjacency_list[u].append(v)
# print(adjacency_list)
for i in range(1,N+1):
    if len(adjacency_list[i])==0:
        dp[i]=0
# print(dp)
for i in range(1,N+1):
    if (visited[i]==0):
        path(i)
print(max(dp))