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: Runtime Error)

def breakBridge(a, l, r, max)
	(l + 1).upto(r - 1) do |i|
		if a[i] < max
			breakBridge(a, i, (a[i] > r) ? r : a[i], max)
			break
		end
	end
	a[l] = max
end

n, m = gets.chomp.split(' ').map{|i| i.to_i}
a = Array.new(n + 1, n + 1)
cnt = 0
m.times do |i|
	idx, b = gets.chomp.split(' ').map{|j| j.to_i}
	a[idx] = (a[idx] > b) ? b : a[idx]
end
1.upto(n) do |i|
	if a[i] <= n
		breakBridge(a, i, a[i], n + 1)
		cnt += 1
	end
end
puts cnt