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
    
    $in = explode(" ", trim(fgets(STDIN)));
    $num_spots = $in[0];
    $num_routes = $in[1];
    $spots = explode(" ", trim(fgets(STDIN)));
    array_unshift($spots, 0);
    
    $i = 1;
    while($i < $num_routes+1) {
        $routes[$i] = explode(" ", trim(fgets(STDIN)));
        ++$i;
    }

    $i = 1;
    while($i < $num_spots+1) {
        $max[$i] = $spots[$i];
        
        $j = 1;
        while($j < $num_routes+1) {
            if($routes[$j][0] == $i) {
                $max[$i] = max($max[$i], $spots[$routes[$j][1]]);
            } elseif($routes[$j][1] == $i) {
                $max[$i] = max($max[$i], $spots[$routes[$j][0]]);
            }
            ++$j;
        }
        ++$i;
    }
    
    $count = 0;
    $i = 1;
    while($i < $num_spots+1) {
        if($max[$i] <= $spots[$i]) {
            ++$count;
        }
        ++$i;
    }

    echo $count;
    
?>