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 Scala (2.11.7) (judge verdict: Accepted)

object Main {

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)
    val N, M = sc.nextInt()
    val G = Array.fill[List[Int]](N+1)(Nil)
    (0 until M) foreach { _ =>
      val u, v = sc.nextInt()
      G(u) = v :: G(u)
    }

    val dp = Array.fill(N+1)(-1)
    val stack = new scala.collection.mutable.Stack[Int]
    (1 to N) foreach { u =>
      if (dp(u) == -1) {
        stack.push(u)
        while (stack.nonEmpty) {
          val u = stack.pop()
          if (u < 0) {
            dp(-u) = 0
            G(-u).foreach { v =>
              dp(-u) = dp(-u) max (dp(v) + 1)
            }
          } else {
            stack.push(-u)
            G(u).foreach { v =>
              if (dp(v) == -1)
                stack.push(v)
            }
          }
        }
      }
    }
    println(dp.max)
  }

}