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 PYTHON):

Solution:
N, M = map(int,raw_input().split())
gra = [set() for n in range(N)]
ins = [0] * N

start = set(range(N))
for m in range(M) :
  x, y = map(int,raw_input().split())
  gra[x-1].add(y-1)
  ins[y-1] += 1
  start.discard(y-1)

mem = [None for n in range(N)]
q = list(start)
for i in q : mem[i] = 0

longest = 0
while q :
  cur = q.pop(0)
  for nxt in gra[cur] :
    ins[nxt] -= 1
    if ins[nxt] == 0 :
      mem[nxt] = mem[cur] + 1
      longest = max(longest, mem[nxt])
      q.append(nxt)

print longest