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: Accepted)

N,M = map(int,input().split(" "))
inedge = [0] * N
edge = [ [] for _ in range(N) ]
for i in range(M):
    x,y = map(int,input().split(" "))
    inedge[y-1] += 1
    edge[x-1].append(y-1)

stack = []
for i in range(N):
    if inedge[i] == 0:
        stack.append((i,0))

ans = [0] * N
while len(stack) != 0:
    nextVer,passLen = stack.pop()
    for e in edge[nextVer]:
        inedge[e] -= 1
        ans[e] = max(ans[e],passLen+1)
        if inedge[e] == 0:
            stack.append((e,ans[e]))

print(max(ans))