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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

# ABC 166 C - Peaks
# https://atcoder.jp/contests/abc166/tasks/abc166_c

# AC
# https://atcoder.jp/contests/abc166/submissions/12807993

n, m = gets.split(/ /).map(&:to_i)
h = gets.split(/ /).map(&:to_i)
ab_s = Array.new(m) { gets.split(/ /).map(&:to_i) }

class Observatory
  def initialize(index, height)
    @index = index
    @height = height

    @connected_observatories = []
  end

  attr_reader :height, :connected_observatories

  def connect_to(observatory)
    connected_observatories.push(observatory)
  end

  def connected_to?(observatory)
    connected_observatories.include?(observatory)
  end

  def good?
    connected_observatories.empty? || connected_observatories.all? { |observatory| height > observatory.height }
  end
end

observatories = h.map.with_index(1) { |height, i| Observatory.new(i, height) }

ab_s.each do |ab|
  a, b = ab

  observatory_a = observatories[a - 1]
  observatory_b = observatories[b - 1]

  observatory_a.connect_to(observatory_b) unless observatory_a.connected_to?(observatory_b)
  observatory_b.connect_to(observatory_a) unless observatory_a.connected_to?(observatory_a)
end

puts observatories.select(&:good?).size