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)
a = []
b = []
count = 0
a_bridge = 0
b_bridge_min = 0
b_bridge_max = 0

m.times do |i|
  a_num, b_num = gets.split.map(&:to_i)
  a.push(a_num)
  b.push(b_num)
end

a.sort!
b.sort!

m.times do |i|
  if i == 0
    a_bridge = a[0]
    b_bridge_min = b[0]
    b_bridge_max = b[0]
    count = 1
  end

  if a_bridge < a[i]
    a_bridge = a[i]
    if b_bridge_min < b[i]
      if a_bridge >= b_bridge_min && a_bridge <= b_bridge_max
        count += 1
      end
    else
      b_bridge_min = b[i]
    end
  elsif a_bridge >= a[i]
    if b_bridge_min > b[i]
      b_bridge_min = b[i]
    else
      b_bridge_max= b[i]
    end
  end
end

puts count