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: Wrong Answer)

# https://atcoder.jp/contests/abc166/tasks/abc166_c
# at_coder_friends test-all C.rb
# require 'pry'

N, M = gets.split.map(&:to_i)
Hs = gets.split.map(&:to_i)
As = Array.new(M)
Bs = Array.new(M)
m_h = Hash.new{|h,k| h[k] = []}
M.times do |i|
  As[i], Bs[i] = gets.split.map(&:to_i)
  m_h[As[i]] << Bs[i]
  m_h[Bs[i]] << As[i]
end

#p "m_h=#{m_h}"

fond_indexes = []
N.times do |i|
  hs = m_h[i+1]
  myh = Hs[i]
  if hs.size > 0
    myh_is_highest = hs.all? do |h|
      myh >= Hs[h-1]
    end
    if myh_is_highest
      fond_indexes << i
    end
  end
  #p "i=#{i}, myh=#{myh}, hs=#{hs},fond_indexes=#{fond_indexes}"
end
#p fond_indexes

ans = fond_indexes.size

puts ans