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

fscanf(STDIN, "%d %d", $n, $m);
$h_arr = explode(' ', trim(fgets(STDIN)));
$inputs = [];
for ($i = 0; $i < $m; ++$i) {
    $inputs[] = explode(' ', trim(fgets(STDIN)));
}

$G = array_fill(0, $n, []);
for ($i = 0; $i < $m; ++$i) {
    $G[$inputs[$i][0] - 1][] = $inputs[$i][1] - 1;
    $G[$inputs[$i][1] - 1][] = $inputs[$i][0] - 1;
}
for ($i = 0; $i < $n; ++$i) {
    $G[$i] = array_unique($G[$i]);
}


$cnt = 0;
for ($i = 0; $i < $n; ++$i) {
    if (count($G[$i]) === 0) {
        ++$cnt;
        continue;
    }

    $flg = true;
    foreach ($G[$i] as $a) {

        if ($h_arr[$i] < $h_arr[$a - 1]) {
            $flg = false;
        }
    }
    if ($flg) {
        ++$cnt;
    }
}

echo $cnt;