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.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args){
		try(Scanner sc = new Scanner(System.in)) {

			int n = sc.nextInt();
			int m = sc.nextInt();
			
			int[] heights = new int[n+1];
			
			for(int i = 0 ; i < n ; i++) {
				heights[i] = sc.nextInt();
			}
			
			
			List<HashSet<Integer>> paths = new ArrayList<HashSet<Integer>>(); 
			for(int i = 0 ; i < n ; i++ ) {
				paths.add(new HashSet<Integer>());
			}
			
			Set<String> pathSet = new HashSet<>();
			
			for(int i = 0 ; i < m ; i++ ) {
				int a = sc.nextInt() - 1;
				int b = sc.nextInt() - 1;
				
//				paths[a-1][b-1] = 1;
//				paths[b-1][a-1] = 1;
//				paths.get(a-1).add(b-1);
//				paths.get(b-1).add(a-1);
				
				pathSet.add(a + "_" + b);
				pathSet.add(b + "_" + a);
			}
			
			int total = 0;
			//
			for(int i = 0 ; i < n ; i++ ) {
				
				boolean isGood = true;
				HashSet<Integer> pathes = paths.get(i);
				
				for(int j = 0 ; j < n ; j++ ) {
					if (i == j )
						continue;
					
					if ( pathSet.contains(i + "_" + j) && heights[i] <= heights[j] ) {
						isGood = false;
						break;
					}					
				}
				
				if ( isGood )
					total++;
			}
			
			System.out.println(total);

		}
	}
}