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: Time Limit Exceeded)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        int goodTenbo = 0;
        int N = sc.nextInt();
        int M = sc.nextInt();
        sc.nextLine();

        int[] tenbo = new int[N];
        for (int i = 0; i < N; i++) {
            tenbo[i] = sc.nextInt();
        }
        sc.nextLine();

        Set<Set<Integer>> michi = new HashSet<Set<Integer>>();
        for (int i = 0; i < M; i++) {
            Set<Integer> tmp = new HashSet<Integer>();
            int a = sc.nextInt();
            int b = sc.nextInt();
            tmp.add(a);
            tmp.add(b);
            michi.add(tmp);
        }

        for (int i = 1; i <= N; i++) {
            int tenbocheck = 0;
            int s = 0;
            for (Set<Integer> m : michi) {
                Set<Integer> tmp = new HashSet<Integer>(m);
                if (tmp.contains(i)) {
                    tmp.remove(i);
                    int x = tmp.iterator().next();
                    if (tenbo[i-1] <= tenbo[x-1]){ tenbocheck++;}
                    if (tenbocheck != 0) { break; }
                }
            }
            if (tenbocheck == 0) {
                goodTenbo++;
            }
        }

        System.out.println(goodTenbo);
    }
}