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 collections import defaultdict
import sys
sys.setrecursionlimit(1000000)

n, m = [int(i) for i in raw_input().split()]
parents = defaultdict(list)

i = 0
while i < m:
    u, v = [int(x) for x in raw_input().split()]
    parents[v-1].append(u-1)
    i += 1

def calc_f(parents, f, i):
    if i < 0 or i >= len(f):
        return 0

    if f[i] != -1:
        return f[i]

    f[i] = 0
    for v in parents[i]:
        f[i] = max(f[i], calc_f(parents, f, v)+1)

    return f[i]

f = [-1] * n
j = 0
while j < n:
    calc_f(parents, f, j)
    j += 1

if len(f) == 0:
    print 0
else:
    print max(f)