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 random
from collections import defaultdict
import sys
sys.setrecursionlimit(100000000)

N, M = map(int, raw_input().split())
# N, K = 5000, 100
AN = defaultdict(list)
for i in range(M):
    u, v = map(int, raw_input().split())
    AN[u].append(v)
longest_path_from_vertex_cache = {}

def get_longest_path(V):


    if V in longest_path_from_vertex_cache:
        return longest_path_from_vertex_cache[V]

    adjacent_vertices = AN[V]
    longest_path = 0
    for vertex in adjacent_vertices:
        current_path_len = 1 + get_longest_path(vertex)
        if longest_path < current_path_len:
            longest_path = current_path_len

    longest_path_from_vertex_cache[V] = longest_path
    return longest_path

print max(get_longest_path(vertex) for vertex in range(1, N+1))