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)

b = []
b = gets.split.map(&:to_i)
c = []
while s = gets
  c.push(s.split.map(&:to_i))
end
d = []
d = c.sort {|a,b| a[1] <=> b[1]}
#p c
#p d
s = 0
t = d[0][1]-1
u = 0
v = 0
cnt = 0
while s <= d.length-1 do
    for i in s..d.length-1 do
        if t < d[i][1]-1
            cnt += 1
            t = d[i][1]-1
            s = i
            break
        end
    end
    #p "#{s} #{t} #{cnt}"
    while d[s][0]-1 <= t do
        s += 1
        if s == d.length 
            break
        end
    end
    cnt += 1
    if s != d.length
        t = d[s][1]
    end
    #p "#{s} #{t} #{cnt}"
    #s -= 1
    #if s != d.length
        #t = d[s-1][0]
        #cnt += 1
    #end
    #p s
end
if t < d[s-1][1]-1
    cnt += 1
end
puts cnt