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: Wrong Answer)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
      	Integer H[] = new Integer[N];
      	for(int i=0;i<N;i++){
          H[i] = sc.nextInt();
          
        }
      	
      	Integer A[] = new Integer[M];
      	Integer B[] = new Integer[M];
        for(int j=0;j<M;j++){
          int A0 = sc.nextInt();
          int B0 = sc.nextInt();
          int A1 = 0;
          int B1 = 0;
          if(B0 < A0) {
            A1 = B0; 
            B1 = A0;
          } 
          else {
            A1 = A0; 
            B1 = B0;
          }
          A[j] = A1;
          B[j] = B1;
        }
      	Set<Integer> num = new HashSet<>();
      	for(int i=0;i<N;i++){
          if(Arrays.asList(A).contains(i+1) || Arrays.asList(B).contains(i+1)){
          for(int j=0;j<M;j++){
            if(A[j] == i+1){
              if(H[A[j]-1] > H[B[j]-1]) num.add(i);
            }
            else if(B[j] == i+1){
              if(H[B[j]-1] > H[A[j]-1]) num.add(i);
            }            
          }
          }
          else num.add(i);
        }
      	
 	      System.out.println(num.size());
    }
}