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: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>

int uf[100000];

int root(int n){
    return uf[n] == n ? n : (uf[n] = root(uf[n]));
}

void marge(int a,int b){
    int pa = root(a);
    int pb = root(b);
    if(pa == pb)return;
    uf[pa] = pb;
}


int main(void){
    register int i;
    int n,m;
    scanf("%d%d",&n,&m);
    long h[n];
    for(i = 0;i < n;i++)scanf("%ld",&h[i]);
    for(i = 0;i < n;i++)uf[i] = i;
    for(i = 0;i < m;i++){
        int a,b;
        scanf("%d%d",&a,&b);
        a--; b--;
        marge(a,b);
    }
    int cnt = 0;
    long maxs[n];
    for(i = 0;i < n;i++)maxs[i] = 0;
    for(i = 0;i < n;i++)if(maxs[uf[i]] < h[i])maxs[uf[i]] = h[i];
    for(i = 0;i < n;i++)if(maxs[i])cnt++;
    printf("%d",cnt);
}