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: Accepted)

def main
  islands_num, req_num = ARGF.gets.split.map(&:to_i)

  # ソートしない解法 ※islands_num分のArrayを最初から用意しておくだけ
  # ※ソートする解法と比べて 229ms -> 192ms と速くなったが、12664kb->15740kb とメモリー使用量は増えた
  requests = Array.new(islands_num)
  req_num.times do
    a, b = ARGF.gets.split.map(&:to_i)
    # 配列indexは0始まりである点に注意
    if requests[b-1].nil?
      requests[b-1] = [a]
    else
      requests[b-1] << a
    end
  end

  # 切断した場所 例）1の場合、1-2 の間を切断したという意味
  last = 0

  # 配列のindexを b に変換するために with_index(1) により1始まりにしている
  # ※それが必要ない場合には each_with_index のほうがいいかも。
  cnt = requests.each.with_index(1).inject(0) do |cnt, (as, i)|
    if !as.nil?
      as.each do |a|
        if last < a
          last = i - 1
          cnt += 1
        end
      end
    end
    cnt
  end

  puts cnt
end

if __FILE__ == $0
  main
end