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 Lua (5.3.2) (judge verdict: Accepted)

local n, m = io.read("*n", "*n")
local edge = {}
local cnt = {}
local len = {}
for i = 1, n do
  edge[i] = {}
  cnt[i] = 0
  len[i] = 0
end
for i = 1, m do
  local x, y = io.read("*n", "*n")
  table.insert(edge[x], y)
  cnt[y] = cnt[y] + 1
end
local tasks = {}
for i = 1, n do
  if cnt[i] == 0 then
    table.insert(tasks, i)
  end
end
local mma = math.max
while 0 < #tasks do
  local src = tasks[#tasks]
  table.remove(tasks)
  for i = 1, #edge[src] do
    local dst = edge[src][i]
    len[dst] = mma(len[dst], len[src] + 1)
    cnt[dst] = cnt[dst] - 1
    if cnt[dst] == 0 then
      table.insert(tasks, dst)
    end
  end
end
local ret = 0
for i = 1, n do
  ret = mma(ret, len[i])
end
print(ret)