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())
dp = [0] * n
indeg = [0] * n
to = [[] for _ in range(n)]
for _ in range(m):
    x, y = map(int, input().split())
    x -= 1
    y -= 1
    to[x].append(y)
    indeg[y] += 1
avail = list(filter(lambda i: indeg[i] == 0, range(n)))
while avail:
    u = avail.pop()
    for v in to[u]:
        dp[v] = max(dp[v], dp[u] + 1)
        indeg[v] -= 1
        if indeg[v] == 0:
            avail.append(v)
print(max(dp))