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)

#!/snap/bin/pypy3

MEMO = dict()

def search(n, data):
    global MEMO
    
    if n in MEMO:
        return MEMO[n]
    else:
        startfrom_n = [element[1] for element in data if element[0] == n]
        if not startfrom_n:
            MEMO[n] = 0
            return 0

        MEMO[n] = max(search(i, data) for i in startfrom_n) + 1
        return MEMO[n]


def main():
    N, M = map(int, input().split())
    data = [tuple(map(int, input().split())) for _ in range(M)]


    print(max(search(n, data) for n in range(1, N+1)))



if __name__ == '__main__':
    main()