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:
n, m = map(int, raw_input().split())
graph = [[] for _ in xrange(n)]
ind = [0 for _ in xrange(n)]
outd = [0 for _ in xrange(n)]
used = [False for _ in xrange(n)]
topo = []
cnt = 0

for i in xrange(m):
    u, v = map(int, raw_input().split())
    ind[v-1] += 1
    outd[u-1] += 1
    graph[u-1].append(v-1)
    
for i in xrange(n):
    if ind[i] == 0 and used[i] == False:
        topo.append(i)
        used[i] = True

while cnt < n:
    u = topo[cnt]
    for v in graph[u]:
        ind[v] -= 1
        if ind[v] == 0 and used[v] == False:
            used[v] = True
            topo.append(v)
    cnt += 1
    
dp = [0 for _ in xrange(n)]
for u in topo:
    for v in graph[u]:
        dp[v] = max(dp[v], dp[u] + 1)
res = max(dp)
print res