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:

""""
5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3
"""

N, M = map(int, raw_input().split())

G = []
for _ in xrange(M):
    G.append(map(int, raw_input().split()))

h = [0]*(N+1)

dest = [[] for _ in xrange(N+1)]

for eg in G:
    h[eg[1]]+=1
    dest[eg[0]].append(eg[1])

que = []

for i in xrange(1, N+1):
    if h[i] == 0: que.append(i)

dp = [0]*(N+1)

while len(que)>0:
    now = que.pop(0)
    for edest in dest[now]:
        h[edest]-=1
        if h[edest]==0:
            que.append(edest)
            dp[edest] = max(dp[now] + 1, dp[edest])

print max(dp)