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:
N, M = map(int, input().split())
xy = [[int(i)-1 for i in input().split()] for _ in range(M)]

cnt = [0] * N
v = [[] for _ in range(N)]
for x, y in xy :
  v[x].append(y)
  cnt[y] += 1
  
s = []
for i in range(N) :
  if cnt[i] == 0 :
    s.append(i)

dp = [0] * N
while s :
  cur = s.pop()
  for nex in v[cur] :
    dp[nex] = max(dp[nex], dp[cur] + 1)
    cnt[nex] -= 1
    if cnt[nex] == 0 :
      s.append(nex)
      
print(max(dp))