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 Kotlin (1.3.71) (judge verdict: Runtime Error)

import java.io.PrintWriter
import java.util.ArrayDeque

fun main(args: Array<String>) {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}

/** edge info */
data class Edge<T>(val to: Int)

fun solve(out: PrintWriter) {
    val (n, m) = readIntegerList()
    val hList = readIntegerList()
    /** graph[fromNodeIndex]: edges to other node */
    val graph = Array(10) { mutableListOf<Edge<Int>>() }
    repeat(m) {
        val (a, b) = readIntegerList().map { it - 1 }
        graph[a].add(Edge(b))
        graph[b].add(Edge(a))
    }

    val isGoodNodeArray = BooleanArray(n) { true }
    val isUnchecked = BooleanArray(n) { true }
    val nodeQueue = ArrayDeque<Int>()
    nodeQueue.addLast(0)
    isUnchecked[0] = false
    while (nodeQueue.isNotEmpty()) {
        val node = nodeQueue.removeFirst()
        for (edge in graph[node]) {
            if (isUnchecked[edge.to]) {
                isUnchecked[edge.to] = false
                nodeQueue.addLast(edge.to)
            }

            if (hList[node] <= hList[edge.to]) {
                isGoodNodeArray[node] = false
            }
        }
    }

    println(isGoodNodeArray.count { it })
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)