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 (2.7.1) (judge verdict: Wrong Answer)

n, m = gets.chomp.split.map(&:to_i)
demands = m.times.map do
  gets.chomp.split.map(&:to_i)
end

min_ranges = demands.group_by(&:first).map do |k, v|
  v.min_by(&:last)
end

cnt = 0
# min_rangesの[0]は単調増加なので、[1]の大小のみに注目する。
min, max = min_ranges[0]
(min_ranges.size - 1).times do |i|
  min = min_ranges[i + 1][0]
  if max >= min_ranges[i + 1][1]
    max = min_ranges[i + 1][1]
  elsif min_ranges[i + 1][0] < max && max <= min_ranges[i + 1][1]
    max = max
  else
     max = min_ranges[i + 1][1]
     cnt += 1
  end
end

puts(cnt + 1)