Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

def rec(v, g, dp)
  return dp[v] if dp[v] != -1
  res = 0
  g[v].each do |nv|
    d = rec(nv, g, dp) + 1
    res = d if d > res
  end
  dp[v] = res
end

n, m = gets.split.map(&:to_i)
g = Array.new(n+1){[]}
dp = Array.new(n+1){-1}
m.times do
  x, y = gets.split.map(&:to_i)
  g[x] << y
end

ans = 0
(1..n).each do |v|
  d = rec(v, g, dp)
  ans = d if d > ans
end
puts ans