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: Time Limit Exceeded)

input = STDIN.read.split("\n")
nums = input[0].split(' ').map{|v| v.to_i}
conflicts = input.slice(1..-1).map{|c| c.split(' ').map{|v| v.to_i}}

bridges_num = nums[0] - 1
conflict_num = nums[1]

break_count = 0

while conflicts.length > 0
  counts = Array.new(bridges_num).map{0}
  max_conflicts = 0
  max_index = 0

  conflicts.each do |v|
    start_bridge = v[0] - 1
    end_bridge = v[1] - 1

    i = start_bridge
    while i < end_bridge
      ct = counts[i] + 1
      if ct > max_conflicts
        max_conflicts = ct
        max_index = i
      end
      counts[i] = ct
      i = i + 1
    end
  end

  conflicts = conflicts.select{|v| !((v[0] - 1) <= max_index && (v[1] - 1) > max_index)}
  break_count = break_count + 1
end

print break_count