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: Accepted)

def tps(n,inCnt,out)
	s = []
	ret = []
	n.times do |i|
		s << i if inCnt[i] == 0
	end
	while v = s.shift
		ret << v
		#tの出力辺とその先のノードmを見て、辺を削除
		#mが入力辺を持っていない=mの最後の入力がtならm追加
		out[v].each do |m|
			inCnt[m] -= 1
			s << m if inCnt[m] == 0
		end
	end
	return ret
end

N,M = gets.split.map(&:to_i)
dp = [0]*(N+1)
cnt= [0]*(N+1)
cnt[0] = -1

vin = (N+1).times.map{[]}
vout = (N+1).times.map{[]}

M.times do
	x,y = gets.split.map(&:to_i)
	cnt[y] += 1
	vin[y] << x
	vout[x] << y
end

list = tps(N+1,cnt,vout)

list.each do |t|
	max = -1
	vin[t].each do |j|
		max = dp[j] if max < dp[j]
	end
	dp[t] = max+1
	#p [t,vin[t],dp[t]]
end
p dp.max