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())

path = [[] for _ in range(N)]
pin = [0]*N
for _ in range(M):
  ip,op = map(int,input().split())
  pin[op-1]+=1
  path[ip-1].append(op-1)

cur = []
for i in range(N):
  if pin[i]==0:
    cur.append(i)

ans = 0
while cur:
  ans += 1
  nxt = []
  for ip in cur:
    for op in path[ip]:
      pin[op] -= 1
      if pin[op]==0 and not(op in nxt):
        nxt.append(op)
  cur = [x for x in nxt]
print(ans-1)