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())
inc = [0]*n
out = [[] for _ in range(n)]
for _ in range(m):
  a, b = map(int, input().split())
  a -= 1
  b -= 1
  out[a].append(b)
  inc[b] += 1

S = {i for i, c in enumerate(inc) if c == 0}
L = []
 
while S:
    k = S.pop()
    L.append(k)
    for m in out[k]:
        inc[m] -= 1
        if inc[m] == 0:
            S.add(m)

dp = [0]*n
for i in L:
  for j in out[i]:
    dp[j] = max(dp[j], dp[i]+1)
print(max(dp))