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 Python (3.8.2) (judge verdict: Runtime Error)

#!python3

LI = lambda: list(map(int, input().split()))

# input
N, M = LI()
XY = [LI() for _ in range(M)]

w = [None] * N
links = [[] for _ in range(N)]
visit = [False] * N


def create_links():
    for x, y in XY:
        links[x - 1].append(y - 1)


def dfs(u):
    visit[u] = True
    n = 0
    for v in links[u]:
        if not visit[v]:
            w[v] = dfs(v)
        n = max(n, w[v])
    return n + 1


def main():
    create_links()
    for i in range(N):
        if not visit[i]:
            w[i] = dfs(i)
    ans = max(w) - 1
    print(ans)


if __name__ == "__main__":
    main()