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: Wrong Answer)

import sys
sys.setrecursionlimit(10 ** 6)
N, M = map(int, input().split())
G = [[] for i in range(N)]
for i in range(M):
    x, y = map(int, input().split())
    x, y = x - 1, y - 1
    G[x].append(y)

d = [-1] * N


def dfs(u, d1):
    if d[i] != -1:
        return d[i]

    ma = 0
    for w in G[u]:
        ma = max(ma, dfs(w, d1 + 1)) + 1

    d[i] = ma
    return ma

ans = 0
for i in range(N):
    ans = max(ans, dfs(i, 0))

print(ans)