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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

module sub
	implicit none
contains
subroutine heapsort2(n,array,turn)
  implicit none
  integer,intent(in)::n
  integer,intent(out)::turn(1:n)
  integer,intent(inout)::array(1:n)
  
  integer::i,k,j,l,m
  double precision::t
  
  if(n.le.0)then
     write(6,*)"Error, at heapsort"; stop
  endif
  if(n.eq.1)return

  do i=1,N
     turn(i)=i
  enddo

  l=n/2+1
  k=n
  do while(k.ne.1)
     if(l.gt.1)then
        l=l-1
        t=array(l)
        m=turn(l)
     else
        t=array(k)
        m=turn(k)
        array(k)=array(1)
        turn(k)=turn(1)
        k=k-1
        if(k.eq.1) then
           array(1)=t
           turn(1)=m
           exit
        endif
     endif
     i=l
     j=l+l
     do while(j.le.k)
        if(j.lt.k)then
           if(array(j).lt.array(j+1))j=j+1
        endif
        if (t.lt.array(j))then
           array(i)=array(j)
           turn(i)=turn(j)
           i=j
           j=j+j
        else
           j=k+1
        endif
     enddo
     array(i)=t
     turn(i)=m
  enddo

  return
end subroutine heapsort2
end module sub



program main
	use sub
	implicit none
	integer :: N, M, i, j, counter
	integer, allocatable :: a(:), b(:), turn(:)
	read(*, *) N, M
	allocate(a(1:M))
	allocate(b(1:M))
	allocate(turn(1:M))
	do i = 1, M
		read(*, *) a(i), b(i)
	end do
	
	call heapsort2(M,a,turn)
	j = 1
	counter = 0
	do i = 1, M
	if(a(j) /= a(i)) then
		if(b(turn(j)) < a(i)) then
			counter = counter + 1
			j = i
		else if(b(turn(j)) > b(turn(i))) then
			j = i
		end if
	end if
	end do
	write(*, *) counter
end program main