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 sys
sys.setrecursionlimit(1000000)
n,m=map(int,input().split())
path=[[] for i in range(n)]
for i in range(m):
  x,y=map(int,input().split())
  # どこからくるかとういう情報
  path[y-1].append(x-1)

memo = [-1]*n
def dfs(v):
  if memo[v] < 0:
    if len(path[v])==0:
      memo[v]=0
    else:
      memo[v]=max([dfs(p)+1 for p in path[v]])
  return memo[v]

res = 0
for i in range(n):
  tmp = dfs(i)
  if res < tmp:
    res = tmp
print(res)