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 (7.3.0) (judge verdict: Runtime Error)

n, m = list(map(int, input().split()))

graph = {i:{} for i in range(n+1)}

visited = [0 for i in range(n+1)]
dp = [0 for i in range(n+1)]


for i in range(m):
    x, y = list(map(int, input().split()))

    graph[x][y] = 1


def dfs(node, graph):
    visited[node] = 1

    for i in graph[node].keys():
        if visited[i] != 1:
            dfs(i, graph)
        
        dp[node] = max(dp[node], 1 + dp[i])

for ele in range(1, n+1):
    if visited[ele] != 1:
        dfs(ele, graph)

# print(dp)
print(max(dp))