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: Accepted)

#include <iostream>
#include <math.h>
#include <stdio.h>
#include <map>

using namespace std;


int main(){

	long long N,M;
	cin>>N>>M;
	long long H[N];
	int highest[N];
	for(int i=0;i<N;i++){
		highest[i]=1;
	}
	long long A[M],B[M];
	long long AA[M],BB[M];
	for(int i=0;i<N;i++){
		cin>>H[i];
	}
	for(int i=0;i<M;i++){
		cin>>AA[i]>>BB[i];
		A[i]=AA[i]-1;
		B[i]=BB[i]-1;
	}

	for(int i=0;i<M;i++){
		if(H[A[i]]>H[B[i]]){
			highest[B[i]]=0;
		}else if(H[A[i]]<H[B[i]]){highest[A[i]]=0;
		}else{
			highest[A[i]]=0;
			highest[B[i]]=0;
		}
	}
	long long ryo=0;
	for(int i=0;i<N;i++){
		ryo=ryo+highest[i];
	}

	cout<<ryo<<endl;


}