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: Wrong Answer)

#!/usr/bin/env python3

from collections import defaultdict
from heapq import heappush, heappop
import sys

sys.setrecursionlimit(10**6)
input = sys.stdin.buffer.readline
INF = 10 ** 9 + 1  # sys.maxsize # float("inf")


def debug(*x):
    print(*x)


def solve0(N, M, edges):
    path = edges.copy()
    exists = 1
    for i in range(2, M + 1):
        next_path = defaultdict(set)
        for v1 in path:
            for v2 in path[v1]:
                if edges[v2]:
                    next_path[v1].update(edges[v2])
                    exists = i
                    # debug(": i, v1, next_path[v1]", i, v1, next_path[v1])
        if exists != i:
            # no more pathes
            break
        path = next_path
    return exists


def solve(N, M, edges):
    longest = {}

    def get_longest(start):
        if longest.get(start) != None:
            return longest[start]

        next_edges = edges.get(start)
        if not next_edges:
            ret = 0
        else:
            ret = max(get_longest(v) for v in edges[start]) + 1
        longest[start] = ret
        return ret

    return max(get_longest(v) for v in edges)


def solve(N, M, edges):
    import numba
    longest = [-1] * (N + 1)

    def intlist(xs):
        if xs:
            return list(xs)
        else:
            return numba.typed.List()

    edges = [intlist(edges[k]) for k in range(N + 1)]
    @numba.njit
    def get_longest(start, edges):
        if longest[start] != -1:
            return longest[start]

        ret = 0
        for v in edges[start]:
            x = get_longest(v, edges) + 1
            if x > ret:
                ret = x
        longest[start] = ret
        return ret

    ret = 0
    for v in range(N + 1):
        x = get_longest(v, edges)
        if x > ret:
            ret = x
    return ret


def solve(N, M, edges):
    longest = [-1] * (N + 1)

    for i in range(N + 1):
        if not edges[i]:
            longest[i] = 0

    def get_longest(start):
        next = edges[start]
        for v in next:
            if longest[v] == -1:
                longest[v] = get_longest(v)

        ret = max(longest[v] for v in next) + 1
        return ret

    for i in range(N):
        if longest[i] == -1:
            longest[i] = get_longest(i)

    return max(longest[v] for v in edges)


T1 = """
4 5
1 2
1 3
3 2
2 4
3 4
"""


def main():
    N, M = map(int, input().split())
    edges = defaultdict(set)
    for i in range(M):
        v1, v2 = map(int, input().split())
        edges[v1].add(v2)

    print(solve(N, M, edges))


def _test():
    """
    >>> as_input(T1)
    >>> main()
    3
    """
    import doctest
    doctest.testmod()


def as_input(s):
    "use in test, use given string as input file"
    import io
    global read, input
    f = io.StringIO(s.strip())
    input = f.readline
    read = f.read


USE_NUMBA = False
if (USE_NUMBA and sys.argv[-1] == 'ONLINE_JUDGE') or sys.argv[-1] == '-c':
    print("compiling")
    from numba.pycc import CC
    cc = CC('my_module')
    cc.export('solve', solve.__doc__.strip().split()[0])(solve)
    cc.compile()
    exit()
else:
    input = sys.stdin.buffer.readline
    read = sys.stdin.buffer.read

    if (USE_NUMBA and sys.argv[-1] != '-p') or sys.argv[-1] == "--numba":
        # -p: pure python mode
        # if not -p, import compiled module
        from my_module import solve  # pylint: disable=all
    elif sys.argv[-1] == "-t":
        _test()
        sys.exit()
    elif sys.argv[-1] != '-p' and len(sys.argv) == 2:
        # input given as file
        input_as_file = open(sys.argv[1])
        input = input_as_file.buffer.readline
        read = input_as_file.buffer.read

    main()