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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        long[] H = new long[N];
        int[] A = new int[M];
        int[] B = new int[M];
        boolean[] isGood = new boolean[N + 1];
        Arrays.fill(isGood, true);
        int ans = N;

        for (int i = 0; i < H.length; i++) {
            H[i] = sc.nextInt();
        }
        for (int i = 0; i < M; i++) {
            A[i] = sc.nextInt();
            B[i] = sc.nextInt();
            if ((H[A[i] - 1] > H[B[i] - 1]) && (isGood[B[i] - 1])) {
                ans--;
                isGood[B[i] - 1] = false;
                continue;
            }
            if ((H[A[i] - 1] < H[B[i] - 1]) && (isGood[A[i] - 1])) {
                ans--;
                isGood[A[i] - 1] = false;
            }
            if ((H[A[i] - 1] == H[B[i] - 1])) {
                if (isGood[A[i] - 1]) {
                    ans--;
                    isGood[A[i] - 1] = false;
                }
                if (isGood[B[i] - 1]) {
                    ans--;
                    isGood[B[i] - 1] = false;
                }
            }
        }

        System.out.println(ans);
        sc.close();
    }
}