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: Accepted)

# coding: utf-8
def main
  n,m = gets.chomp.split(/ /).map {|i| i.to_i}
  hs = gets.chomp.split(/ /).map {|i| i.to_i}
  hs.unshift(0) #indexを合わせる

  h = Hash.new
  (1..m).each {|j|
    a,b = gets.chomp.split(/ /).map {|i| i.to_i}

    h[a] = [] unless h[a]
    h[b] = [] unless h[b]

    h[a] << b
    h[b] << a
  }

  #p h
  #p hs

  good = []
  (1..n).each {|i|
    rs = h[i]
    rs = [] unless rs
    #next if hs.empty?

    # hの高さ
    hh = hs[i]

    higher = true
    rs.each { |r|
      if hh <= hs[r]
        higher = false
        break
      end
    }

    if higher
      good << i 
    end
  }

  #p good
  x = good.length
  puts x
end

main