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
from collections import deque

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')
in_nl = lambda: list(map(int, readline().split()))
in_nl2 = lambda H: [in_nl() for _ in range(H)]
in_map = lambda: [s == ord('.') for s in readline() if s != ord('\n')]
in_map2 = lambda H: [in_map() for _ in range(H)]
in_all = lambda: map(int, read().split())


def bfs(N, v0, edge):

    d = [-1] * N
    d[v0] = 0
    q = deque()
    q.append(v0)

    while q:
        v = q.popleft()
        for nv in edge[v]:
            q.append(nv)
            d[nv] = max(d[nv], d[v] + 1)

    return max(d)


def v_sort(N, dag):

    degree = [0] * N
    for i in range(N):
        for v in dag[i]:
            degree[v] += 1

    ret = [v for v in range(N) if degree[v] == 0]

    return ret


def main():

    N, M = in_nn()

    edge = [[] for _ in range(N)]
    for i in range(M):
        x, y = in_nn()
        x, y = x - 1, y - 1
        edge[x].append(y)

    vs = v_sort(N, edge)
    ans = 0
    for v in vs:
        ans = max(ans, bfs(N, v, edge))

    print(ans)


if __name__ == '__main__':
    main()