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.Scanner;

public class Main{
	public static void main(String args[]){
		Scanner scan = new Scanner(System.in);
		int N = scan.nextInt();
		int M = scan.nextInt();
		int[] H = new int[N];
		for(int i = 0; i<N;i++) {
			H[i] = scan.nextInt();
		}
		int[] A = new int[M];
		int[] B = new int[M];
		for(int i = 0; i<M;i++) {
			A[i] = scan.nextInt();
			B[i] = scan.nextInt();
		}
		scan.close();
		int good = 0;
		int goodnum = 0;
		int flagnum = -1;
		int flag = -1;

		for(int i = 0;i<N;i++) {
			for(int j = 0;j<M;j++) {
				flagnum = -1;
				if(A[j]-1==i) {
					flagnum = B[j];
				}else if(B[j]-1==i) {
					flagnum = A[j];
				}
				if(flagnum!=-1) {
					if(H[i]>H[flagnum-1]) {
						good++;
					}else if(H[i]<H[flagnum-1]){
						good = -2147483648;
					}
					flag = flagnum;
				}
			}
			if(flag==-1) {
				good++;
			}
			flag = -1;
			if(good>0) {
				goodnum++;
			}
			good = 0;
		}

		System.out.println(goodnum);

	}
}