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: Runtime Error)

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(N)(new scala.collection.mutable.ArrayBuffer[Int]())
    (0 until M) foreach { _ =>
      val u, v = sc.nextInt()
      G(u-1).append(v-1)
    }

    val Inf = Int.MaxValue / 10
    val dp = Array.fill(N)(Inf)
    def recursive(u: Int): Int =
      if (dp(u) != Inf) dp(u)
      else {
        dp(u) = 0
        G(u).foreach { v =>
          dp(u) = (recursive(v) + 1) max dp(u)
        }
        dp(u)
      }

    (0 until N) foreach { u =>
      if (dp(u) == Inf)
        recursive(u)
    }
    println(dp.max)
  }

}