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 sys import stdin, setrecursionlimit as lim

lim(100001)

n, m = map(int, raw_input().strip().split())
inp = stdin.readlines()

g1 = [[] for i in xrange(n + 1)]
g2 = [[] for i in xrange(n + 1)]
ans1 = [0 for i in xrange(n + 1)]
ans2 = [0 for i in xrange(n + 1)]

for line in inp:
    u, v = map(int, line.strip().split())
    g1[u].append(v)
    g2[v].append(u)

def dfs1(u):
    if ans1[u] != 0: return ans1[u]
    ret = 0
    for v in g1[u]:
        if ans1[v] != 0: ret = max(ret, ans1[v])
        else: ret = max(ret, dfs1(v))
    ret += 1
    ans1[u] = ret
    return ans1[u]

def dfs2(u):
    if ans2[u] != 0: return ans2[u]
    ret = 0
    for v in g2[u]:
        if ans2[v] != 0: ret = max(ret, ans2[v])
        else: ret = max(ret, dfs2(v))
    ret += 1
    ans2[u] = ret
    return ans2[u]

ans = 0
for i in xrange(1, n + 1):
    if ans1[i] == 0: ans = max(ans, dfs1(i))
for i in xrange(1, n + 1):
    if ans2[i] == 0: ans = max(ans, dfs2(i))

print ans - 1