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 Python (3.4.3) (judge verdict: Runtime Error)

from collections import defaultdict

def dfs(s, graph, dp, visited):
  visited.add(s)
  if s not in graph:
      dp[s-1] = 0
  for v in graph[s]:
    dfs(v, graph, dp, visited)
    dp[s-1] = max(dp[s-1], 1+dp[v-1])

def main():
  graph = defaultdict(set)
  i = 0

  while True:
    line = input()
    if line:
      s = line.split(' ')
      if i == 0:
        n, m = int(s[0]), int(s[1])
      else:
        u, v = int(s[0]), int(s[1])
        graph[u].add(v)
    else:
      break
    i += 1

  dp = [float('-inf')]*n
  visited = set()
  for i in range(1, n+1):
    if i not in visited:
      dfs(i, graph, dp, visited)
  return max(dp)

if __name__ == '__main__':
  ans = main()
  print(str(ans))