Problem:
Score : 400 points

Problem Statement

There are N islands lining up from west to east, connected by N-1 bridges.

The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.

One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:

Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these M requests.

Find the minimum number of bridges that must be removed.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq a_i < b_i \leq N

All pairs (a_i, b_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the minimum number of bridges that must be removed.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Sample Input 2

9 5
1 8
2 7
3 5
4 6
7 9

Sample Output 2

2

Sample Input 3

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 3

4

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

N, M = gets.split.map(&:to_i)

battle = []
removed = []
remove_count = 0

arr = []
M.times do
  a, b = gets.split.map(&:to_i)
  if b - a == 1
    removed << b-1
    remove_count += 1
  else
    arr << [a, b]
  end
end

arr.each do |a, b|
  add = true
  removed.each do |r|
    if a <= r and r < b
      add = false
      break
    end
  end
  battle << a.upto(b-1).to_a if add
end

while battle.any?
  # puts "BATTLES REMAIN: #{battle}"

  remove_bridge = 0
  max_count = 0
  battle_ids_include_bridge = []

  # puts "SEARCH: #{battle.min_by{|b| b.size}}"  
  battle.min_by{|b| b.size}.each do |n|
    # puts "WILL FIND #{n}"
    num_count = 0
    battle_ids = []
    battle.each.with_index do |battles, id|
      # puts "battles: #{battles}"
      if battles.include?(n)
        # puts "FOUND #{n} !"
        num_count += 1 
        battle_ids << id
      end
    end
    if num_count > max_count
      max_count = num_count
      remove_bridge = n
      battle_ids_include_bridge = battle_ids
    end
    break if max_count == battle.count
    # puts 
  end
  # puts "REMOVE BRIDGE ID: #{remove_bridge}"
  # puts "battle_ids_include_bridge: #{battle_ids_include_bridge}"
  battle_ids_include_bridge.sort.reverse.each do |id|
    battle.delete_at(id)
  end
  remove_count += 1
  # puts "---"
end

puts remove_count