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)

import sys
sys.setrecursionlimit(10**6)
input = sys.stdin.readline
N,M = map(int,input().split())
lst=[{} for f in range(N)]
for i in range(M):
 x,y=map(int,input().split())
 lst[x-1][y-1]=1
memo = {}
def cost(a):
 ans=0
 if a in memo:
  return memo[a]
 else:
  for i in lst[a]: 
   if i in memo:
    ans=max(memo[i]+1,ans)
   else:
    ans=max(cost(i)+1,ans)
  memo[a]=ans
  return ans
T=0
for i in range(N):
 T=max(T,cost(i))
print(T)