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($observatory_count, $load_count) = explode(' ', trim(fgets(STDIN)));

$observatory_height_array = explode(' ', trim(fgets(STDIN)));

// 道が存在しない場合用のチェック配列
$check_array_int = range(1, (int)$observatory_count);
foreach ($check_array_int as $check_no) {
    $check_array[] = (string)$check_no;
}

for ($i = 0; $i < (int)$load_count; $i++) {
    $check_observatory_no = explode(' ', trim(fgets(STDIN)));

    // 出てきた展望台はチェック配列から削除
    $check_array = array_diff($check_array, $check_observatory_no);

    // 対象の展望台の高さを取得
    $observatory1 = $observatory_height_array[(int)$check_observatory_no[0] - 1];
    $observatory2 = $observatory_height_array[(int)$check_observatory_no[1] - 1];

    if ((int)$observatory1 === (int)$observatory2) continue;

    $more_height_array[] = ($observatory1 > $observatory2) ? $observatory1 : $observatory2;
}

if (count($check_array) === 0) {
    echo count(array_unique($more_height_array));
} else {
    echo count(array_unique($more_height_array)) + count($check_array);
}