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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		int N = stdIn.nextInt();
		int M = stdIn.nextInt();
		ArrayList<Long> H = new ArrayList<Long>();
		ArrayList<Integer> A = new ArrayList<Integer>();
		ArrayList<Integer> B = new ArrayList<Integer>();
		for(int i = 0; i < N; i ++) {
			H.add(stdIn.nextLong());
		}
		for(int i = 0; i < M; i ++) {
			A.add(stdIn.nextInt());
			B.add(stdIn.nextInt());
		}
		
		int ans = 0;
		
		for(int i = 0; i < N; i ++) {
			boolean isGood = false;
			int connect = 0;
			for(int j = 0; j < M; j ++) {
				int a = A.get(j) - 1;
				int b = B.get(j) - 1;
				if(i == a) {
					connect ++;
					if(H.get(b) < H.get(a)) {
						isGood = true;
					}else {
						isGood = false;
						break;
					}
				}else if(i == b) {
					connect ++;
					if(H.get(a) < H.get(b)) {
						isGood = true;
					}else {
						isGood = false;
						break;
					}
				}
			}
			if(isGood || connect == 0) {
				ans ++;
			}
		}
		System.out.println(ans);
	}
}