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)

# -*- coding: utf-8 -*-


def main():
    n, m = map(int, input().split())
    graph = [[] for _ in range(n)]
    dp = [-1 for _ in range(10 ** 5 + 10)]

    for _ in range(m):
        xi, yi = map(int, input().split())
        xi -= 1
        yi -= 1
        graph[xi].append(yi)

    # See:
    # https://qiita.com/drken/items/03c7db44ccd27820ea0d#g-%E5%95%8F%E9%A1%8C---longest-path
    def rec(v):
        if dp[v] != -1:
            return dp[v]

        result = 0

        for next_v in graph[v]:
            result = max(result, rec(next_v) + 1)

        dp[v] = result

        return dp[v]

    ans = 0

    for i in range(n):
        ans = max(ans, rec(i))

    print(ans)


if __name__ == '__main__':
    main()