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:
from collections import deque
n,m = map(int, input().split())
rev = [list() for _ in range(n+1)]
tr = [0]*(n+1)
ans = [0]*(n+1)
for _ in range(m):
  x,y = map(int,input().split())
  rev[y].append(x)
  tr[x] += 1
q = deque()
for i in range(1,n+1):
  if tr[i] == 0:
    q.append(i)
while q:
  cur = q.popleft()
  for x in rev[cur]:
    tr[x] -= 1
    ans[x] = max(ans[x],ans[cur]+1)
    if tr[x] == 0:
      q.append(x)
print(max(ans))