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: Time Limit Exceeded)

from sys import setrecursionlimit


def f(i, links, dp):
    if dp[i] != -1:
        return dp[i]
    if len(links[i]) == 0:
        dp[i] = 0
    else:
        dp[i] = max(f(j, links, dp) for j in links[i]) + 1
    return dp[i]


setrecursionlimit(10 ** 6)

N, M = map(int, input().split())

links = [[] for _ in range(N)]
for _ in range(M):
    x, y = map(int, input().split())
    links[x - 1].append(y - 1)

dp = [-1] * N
print(max(f(i, links, dp) for i in range(N)))