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 C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <string.h>
#include <stdbool.h>
#include <stdlib.h>
#include <math.h>
#define _USE_MATH_DEFINES

int main()
{
    int sum=0,N=0,H[100000]={0},M=0,load[100000][2]={0},flag[100000]={0};
    scanf("%d %d",&N,&M);
    for(int i=0;i<N;i++)
	scanf("%d",&H[i]);
    for(int i=0;i<M;i++)
	scanf("%d %d",&load[i][0],&load[i][1]);

    for(int i=0;i<N;i++){
	int bad=0;
	if(flag[i]==1)
	    bad=1;
	for(int j=0;j<M;j++){
	    if(bad==1)
		break;
	    else if(i+1==load[j][0] && H[i]<=H[load[j][1]-1]){
		bad=1;
		break;
	    }
	    else if(i+1==load[j][0] && H[i]>H[load[j][1]-1])
		flag[load[j][1]-1]=1;
	    else if(i+1==load[j][1] && H[i]<=H[load[j][0]-1]){
		bad=1;
		break;
	    }
	    else if(i+1==load[j][1] && H[i]>H[load[j][0]-1])
		flag[load[j][0]-1]=1;
	}
	if(bad==0)
	    sum++;
    }

    printf("%d\n",sum);
    return 0;
}