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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
    list($N,$M) = array_map('intval',explode(" ",trim(fgets(STDIN))));
    
    $height = array_map('intval',explode(" ",trim(fgets(STDIN))));
    array_unshift($height,0);
    
    for($i=1;$i<=$M;$i++){
        list($a,$b) = array_map('intval',explode(" ",trim(fgets(STDIN))));
        
        //無向ぐらふにする。
        $G[$a][] = $b;
        $G[$b][] = $a;
    }
    // sort($G);
    // array_unshift($G,0);
    // var_dump($G);
    
    //全てよい展望台であることとする
    $flg = array_fill(1,$N,1);
    //展望台＄jについて
    for($j=1;$j<=$N;$j++){
        if(empty($G[$j])){
            $flg[$j] = 0;
            goto next;
        }
        foreach((array)$G[$j] as $value){
            //一個でも$jより一か所でも高ければ
            if($height[$j] <= $height[$value]){
                $flg[$j] = 0;
            }
        }
        next:
    }
    echo array_sum($flg)."\n";
?>