Problem: 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.

Examples

Input

4 5
1 2
1 3
3 2
2 4
3 4


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3


Output

3

Solution (in PYTHON3):

Solution:
import collections
import sys
sys.setrecursionlimit(10**9)
cache,edge={},collections.defaultdict(list)
def dp(node):
  if node in cache:
    return cache[node]
  lcl_max=0
  for child in edge[node]:
    
    lcl_max=max(lcl_max,1+dp(child))
  cache[node]=lcl_max
  return lcl_max
 
max_dis=0

n,m=map(int,input().split())
for _ in range(m):
  a,b=map(int,input().split())
  edge[a].append(b)
for node in range(1,n+1):
  max_dis=max(max_dis,dp(node))
print(max_dis)