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: Time Limit Exceeded)

N, M = (int(i) for i in input().split()) 

outs = [[] for i in range(N)]
ins = [0] * N


for _ in range(M):
    x, y = (int(i) for i in input().split())
    x -= 1
    y -= 1
    outs[x].append(y)
    ins[y] += 1

q = []
for i in range(N):
    if ins[i] == 0:
        q.append(i)

result = []
while q != []:
    qn = q.pop(0)
    result.append(qn)
    for v in outs[qn]:
        ins[v] -= 1
        if ins[v] == 0:
            q.append(v)


last = [0] * N
# last[i] = iが最後だったときに最長のパス
for sq in result:
    t = last[sq] + 1
    for v in outs[sq]:
        last[v] = max(last[v], t)

print(max(last))