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:
import itertools as ite
import math
import random
import sys

INF = 10 ** 18
MOD = 10 ** 9 + 7

sys.setrecursionlimit(1000000)

N, M = map(int, raw_input().split())
E = [[] for i in range(N + 1)]
for i in range(M):
    x, y = map(int, raw_input().split())
    E[x].append(y)

m = {}
def func(pos):
    if pos in m:
        return m[pos]
    ret = 0
    for to in E[pos]:
        ret = max(ret, func(to) + 1)
    m[pos] = ret
    return ret

print max(func(i) for i in range(1, N + 1))