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)

def main():
    def DFS(v):
        if DP[v] != -1: return DP[v]

        res = 0
        for i in G[v]:
            res = max(res, DFS(i) + 1)

        DP[v] = res
        return res


    N, M = map(int, input().split())
    xy = [list(map(int, input().split())) for _ in range(M)]

    G = [[] for _ in range(N)]
    for i in range(M):
        G[xy[i][0] - 1].append(xy[i][1] - 1)

    DP = [-1] * N

    ans = 0
    for v in range(N):
        ans = max(ans, DFS(v))

    print(ans)


if __name__ == '__main__':
    main()

exit()