Problem: 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.

Examples

Input

4 3
1 2 3 4
1 3
2 3
2 4


Output

2


Input

6 5
8 6 9 1 2 1
1 3
4 2
4 3
4 6
4 6


Output

3

Solution (in JAVA):

Solution:
import java.util.*;
public class Main{
  public static void main(String[] args){
    Scanner sc =new Scanner(System.in);
    int N =sc.nextInt();
    int M =sc.nextInt();
    long H[] =new long[N];
    int A[] =new int[M];
    int B[] =new int[M];
    int C[] =new int[N];
    long x =0;
    for(int i=0;i<N;i++){
      H[i]=sc.nextLong();}
    for(int j=0;j<M;j++){
      A[j]=sc.nextInt();
      B[j]=sc.nextInt();
      if(H[A[j]-1]>H[B[j]-1]){C[B[j]-1]=-1;}
      else if(H[A[j]-1]==H[B[j]-1]){C[B[j]-1]=-1;C[A[j]-1]=-1;}
      else{C[A[j]-1]=-1;}}
    for(int k=0;k<N;k++){
      if(C[k]==0){x=x+1;}}
    System.out.println(x);
  }
}