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 N = sc.nextInt();
        int M = sc.nextInt();
        int[] H = new int[(int)N];
        int[] A = new int[2];
        int ans = 0;
        
        int[] C = new int[(int) N];
        for(int i = 0; i < N ; i++){
            C[i] = 1;
        }
        
        for(int i = 0 ; i < N ; i++){
                H[i] = sc.nextInt(); 
        }
        
        
        for(int n = 0; n < M ; n++){
            A[0] = sc.nextInt();
            A[1] = sc.nextInt();
            if(H[A[0] - 1] == H[A[1] - 1]){
                C[A[0] - 1] = 0;
                C[A[1] - 1] = 0;
            }else if(H[A[0] - 1] < H[A[1] - 1]){
                C[A[0] - 1] = 0;
            }else{
                C[A[1] - 1] = 0;
            }
            
        }
        
        for(int i = 0; i < N ;i++){
            ans = ans + C[i];
        }        
        System.out.println(ans);
    
    }
}