output_description: Print the length of the longest directed path in G.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M
      x_1 y_1
      x_2 y_2
      :
      x_M y_M
attempt: import sys
  sys.setrecursionlimit(10**6)
  from functools import lru_cache
  @lru_cache(maxsize = None)
  
  edges, vertices = map(int, input().split())
  dp = [None for _ in range(edges)]
  
  nodes = [[] for _ in range(edges)]
  
  for i in range(vertices):
      start, end = map(int, input().split())
      nodes[end -1].append(start-1)
  
  for i in range(edges):
      if not len(nodes[i]):
          dp[i] = 0
  @lru_cache(maxsize = None)
  def find(arr):
      if not len(arr):
          return 0
      for x in arr:
          if dp[x] is None:
              dp[x] = find(nodes[x])
      return 1 + max(dp[x] for x in arr)
  
  for i in range(edges):
      dp[i] = find(nodes[i])
  
  print(max(dp))
  
problem_description: 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.
samples: [{"input": "4 5\n    1 2\n    1 3\n    3 2\n    2 4\n    3 4", "output": "3\n    \n\nThe red directed path in the following figure is the longest:\n\n![](https://img.atcoder.jp/dp/longest_0_muffet.png)\n\n* * *"}, {"input": "6 3\n    2 3\n    4 5\n    5 6", "output": "2\n    \n\nThe red directed path in the following figure is the longest:\n\n![](https://img.atcoder.jp/dp/longest_1_muffet.png)\n\n* * *"}, {"input": "5 8\n    5 3\n    2 3\n    2 4\n    5 2\n    5 1\n    1 4\n    4 3\n    1 3", "output": "3\n    \n\nThe red directed path in the following figure is one of the longest:\n\n![](https://img.atcoder.jp/dp/longest_2_muffet.png)"}]