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 Perl (5.26.1) (judge verdict: Accepted)

use strict;

use strict;

$_ = <>;
chomp;

my ($n, $m) = split(/\s+/);

$_ = <>;
chomp;
my @height = split(/\s+/);

my @way;

for (my $i = 0; $i < $m; $i++) {
    $_ = <>;
    chomp;
    my ($p1, $p2) = split(/\s+/);
    $p1--;
    $p2--;
    if ($way[$p1]) {
	push(@{$way[$p1]}, $p2);
    } else {
	$way[$p1] = [ $p2 ];
    }
    if ($way[$p2]) {
	push(@{$way[$p2]}, $p1);
    } else {
	$way[$p2] = [ $p1 ];
    }
}

my $good = 0;
for (my $i = 0; $i < $n; $i++) {
    if ($way[$i]) {
	my $ng = 0;
	foreach my $p (@{$way[$i]}) {
	    if ($height[$i] > $height[$p]) {
	    } else {
		$ng++;
	    }
	}
	if ($ng == 0) {
	    $good++;
	}
    } else {
	$good++;
    }
}
    
print "$good\n";