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:


from Queue import Queue

n, m = map(int, raw_input().split())
indeg = [0] * n
graph = [[] for _ in range(n)]
for _ in range(m):
    x, y = map(int, raw_input().split())
    graph[x - 1].append(y - 1)
    indeg[y - 1] += 1

cola = Queue()
for i in range(n):
    if indeg[i] == 0:
        cola.put(i)
topsort = []
while not cola.empty():
    v = cola.get()
    topsort.append(v)
    for i in graph[v]:
        indeg[i] -= 1
        if indeg[i] == 0:
            cola.put(i)

dp = [0] * n
for i in range(n - 1, -1, -1):
    v = topsort[i]
    for u in graph[v]:
        dp[v] = max(dp[v], 1 + dp[u])
print(max(dp))