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.chomp.split.map(&:to_i)

list = []
values = Array.new(N + 1, 0)
counter = Array.new(N + 1, 0)

M.times do
  a, b = gets.chomp.split.map(&:to_i)
  list << [a, b]
end

group = list.group_by { |(a, b)| a }
lands = group.map { |k, v| [k, v.map(&:last).min] }

ans = 0

min = lands.first[0]
max = lands.first[1]

cut_point = 0

lands.each do |from, to|
  if !(min..max).cover?(from..to) && from <= max
    if from < max
      cut_point = max - 1
    end

    ans += 1
  end

  min = from
  max = to
end

if cut_point <= lands.last.first
  ans += 1
end

puts ans