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)

require "scanf"

n, m = gets.scanf("%d %d")

a_s = []
b_s = []

req = []
m.times do
    a,b = gets.scanf("%d %d")
    a_s << a
    b_s << b
    req << (a..b)
end

def inter r
    (r.min..r.max-1)
end

def overlaps? a, b
    inter(b).each do |i|
        if inter(a).include?(i)
            return true
        end
    end
    false
end

# 
count = 0
n.times do
    arr = Array.new(n){0}
    req.each do |r|
        inter(r).each do |i|
            arr[i]+=1
        end
    end
    cut = arr.index(arr.max)
    f=false
    (0...req.size).to_a.reverse.each do |i|
        if( inter(req[i]).include?(cut) )
            req.delete_at(i)
            f = true
        end
    end
    count += 1 if f
end

p count