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 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
public class Main {
	public static void main(String[] args){

		Scanner sc = new Scanner(System.in);

		int towerCount = sc.nextInt();
		int roadCount = sc.nextInt();

		int[] towerHeight = new int[towerCount];
		for (int i = 0; i < towerCount; i++) {
			towerHeight[i] = sc.nextInt();
		}

		boolean[] towerJudge = new boolean[towerCount];
		for (int i = 0; i < towerCount; i++) {
			towerJudge[i] = true;
		}

		int[] towerA = new int[roadCount];
		int[] towerB = new int[roadCount];
		for (int i = 0; i < roadCount; i++) {
				towerA[i] = sc.nextInt();
				towerB[i] = sc.nextInt();

				towerA[i]--;
				towerB[i]--;

				if(towerHeight[towerA[i]] <= towerHeight[towerB[i]]) {
					towerJudge[towerA[i]] = false;
				}

				if(towerHeight[towerB[i]] <= towerHeight[towerA[i]]) {
					towerJudge[towerB[i]] = false;
				}
		}

		int goodTowerCount = 0;


		for (int i = 0; i < towerCount; i++) {
			if (towerJudge[i]) {
				goodTowerCount++;
			}
		}

		System.out.print(goodTowerCount);

	return;

	}
}