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 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
n, m = map(int, input().split())
edges = [[]for _ in range(n)]
for _ in range(m):
    x, y = map(lambda x: int(x)-1, input().split())
    edges[x].append(y)


def dfs(v, parent):
    visited[v] = 1
    for v2 in edges[v]:
        if v2 == parent:
            continue
        dfs(v2, v)
        if dist[v] >= dist[v2]+1:
            continue
        dist[v] = dist[v2]+1


dist = [0]*n
visited = [0]*n

for i in range(n):
    if visited[i]:
        continue
    dfs(i, -1)

print(max(dist))