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)

N, M = map(int, input().split())
edge = {}
starts = set(i for i in range(1, N+1))
for _ in range(M):
    x, y = map(int, input().split())
    if x not in edge:
        edge[x] = [y]
    else:
        edge[x].append(y)
    starts -= {y}

def rec(d, e, dp):
    dp[e] = max(dp[e], d)
    if e not in edge:
        return 0
    for f in edge[e]:
        rec(d+1, f, dp)
    return max(dp)

depth = []
for s in starts:
    depth.append(rec(0, s, [0]*(N+1)))
print(max(depth))