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)

import sys
input = sys.stdin.readline
inf = float('inf')
mod = 10**9+7


def MI(): return map(int, input().split())


def LI(): return list(mi())


def LI_(): return [int(x) - 1 for x in input().split()]


def LIN(n: int): return [input() for _ in range(n)]


def LLIN(n: int): return [li() for _ in range(n)]


def LLIN_(n: int): return [li_() for _ in range(n)]


def LLI(): return [list(map(int, l.split())) for l in input()]


def I(): return int(input())


def F(): return float(input())


def ST(): return input().replace('\n', '')


def main():
    N, M = MI()
    edge = [[] for _ in range(N)]
    for _ in range(M):
        x, y = LI_()
        edge[x].append(y)

    def go_to_leaf(n):
        if dp[n] >= 0:
            return dp[n]
        ret = 0
        for y in edge[n]:
            ret = max(go_to_leaf(y) + 1, ret)
        dp[n] = ret
        return ret

    dp = [-1] * N
    ans = 0
    for i in range(N):
        ans = max(ans, go_to_leaf(i))
    print(ans)

    """start = 0
    while rev_edge[start]:
        start = rev_edge[start][0]
    stack = set([start])
    ans = 0
    for _ in range(N + 1):
        tmp = []
        print(stack)
        while stack:
            now = stack.pop()
            tmp.extend(edge[now])
        if not tmp:
            print(tmp)
            break
        stack = set(tmp)
        ans += 1
    print(ans)"""


if __name__ == '__main__':
    main()