Problem:
Score : 300 points

Problem Statement

There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i.
There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j.

Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road.
Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road.

How many good observatories are there?

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq H_i \leq 10^9

1 \leq A_i,B_i \leq N

A_i \neq B_i

Multiple roads may connect the same pair of observatories.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
H_1 H_2 ... H_N
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Print the number of good observatories.

Sample Input 1

4 3
1 2 3 4
1 3
2 3
2 4

Sample Output 1

2

From Obs. 1, you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3, so Obs. 1 is not good.

From Obs. 2, you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3, so Obs. 2 is not good.

From Obs. 3, you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2, so Obs. 3 is good.

From Obs. 4, you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2, so Obs. 4 is good.

Thus, the good observatories are Obs. 3 and 4, so there are two good observatories.

Sample Input 2

6 5
8 6 9 1 2 1
1 3
4 2
4 3
4 6
4 6

Sample Output 2

3

Solution in Scala (2.13.1) (judge verdict: Accepted)

import java.util.Scanner

import scala.collection.mutable

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt()
  val m = sc.nextInt()
  val heights = new mutable.HashMap[Int, Int]()
  (1 to n).foreach { i =>
    val h = sc.nextInt()
    heights.put(i, h)
  }
  val lines = (1 to m).map { _ => Line(sc.nextInt(), sc.nextInt()) }
  val groupedLines = new mutable.HashMap[Int, List[Int]]
  addGroupedLines(lines)
  val result = (1 to n).count { i =>
    val height = heights(i)
    val tos = groupedLines.getOrElse(i, Nil)
    val result = tos.forall { to => heights(to) < height }
    result
  }
  println(result)

  def addGroupedLines(lines: Seq[Line]): Unit = {
    lines.foreach { line =>
      groupedLines.put(line.a, line.b :: groupedLines.getOrElse(line.a, Nil))
      groupedLines.put(line.b, line.a :: groupedLines.getOrElse(line.b, Nil))
    }
  }
}

case class Line(a: Int, b: Int)