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: Time Limit Exceeded)

import scala.collection.mutable

object Main extends App {

  import scala.io.StdIn._

  val Array(n, m) = readLine.trim.split(' ').map(_.toInt)
  val edges = Array.tabulate(n){_ ⇒ Nil: List[Int]}
  val inEdge = Array.tabulate(n){_ ⇒ 0}
  for (_ ← 0 until m){
    val Array(x, y) = readLine.trim.split(' ').map(_.toInt)
    edges(x - 1) ::= y - 1
    inEdge(y - 1) += 1
  }
  val longestPath = Array.tabulate(n){_ ⇒ n}
  val queue = mutable.PriorityQueue()(Ordering.by[(Int, Int), Int](_._2).reverse)
  inEdge.indices.filter(p ⇒ inEdge(p) == 0).foreach(p ⇒ queue.enqueue((p, n)))
  while (queue.nonEmpty){
    val (top, cost) = queue.dequeue()
    if (longestPath(top) == cost) {
      for (next ← edges(top)) {
        if (longestPath(next) > cost - 1) {
          longestPath(next) = cost - 1
          queue.enqueue((next, cost - 1))
        }
      }
    }
  }
  println(n - longestPath.min)
  implicit class Extend[T](value: T){
    def also(func: T ⇒ Unit): T = {func(value); value}
    def let[A](func: T ⇒ A): A = func(value)
  }
}