Problem:
Score : 400 points

Problem Statement

There are N empty boxes arranged in a row from left to right.
The integer i is written on the i-th box from the left (1 \leq i \leq N).

For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.

We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:

For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.

Does there exist a good set of choices? If the answer is yes, find one good set of choices.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

a_i is 0 or 1.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

If a good set of choices does not exist, print -1.

If a good set of choices exists, print one such set of choices in the following format:

M
b_1 b_2 ... b_M

where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.

Sample Input 1

3
1 0 0

Sample Output 1

1
1

Consider putting a ball only in the box with 1 written on it.

There are three boxes with multiples of 1 written on them: the boxes with 1, 2, and 3. The total number of balls contained in these boxes is 1.

There is only one box with a multiple of 2 written on it: the box with 2. The total number of balls contained in these boxes is 0.

There is only one box with a multiple of 3 written on it: the box with 3. The total number of balls contained in these boxes is 0.

Thus, the condition is satisfied, so this set of choices is good.

Sample Input 2

5
0 0 0 0 0

Sample Output 2

0

Putting nothing in the boxes can be a good set of choices.

Solution in Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

module queue
  implicit none
  type :: JagArray
    integer,allocatable :: array(:)
  end type JagArray
  contains
  subroutine push(A,b)
    integer,allocatable,dimension(:)::A
    integer::b
    A=[A,b]
  end subroutine
  subroutine pop(A)
  	integer,allocatable,dimension(:)::A
    A=A(2:)
  end subroutine
end module queue

use queue
integer N
integer,allocatable,dimension(:)::A,B,C
integer presum
read*,N
allocate(A(N),B(N))
read*,A
B=0
C=[integer::]
if(A(N)==1)then
  B(N)=1
  C=[N,c]
endif
do i=n-1,1,-1
  presum=0
  j=i+i
  do while(j<=N)
    presum=presum+B(j)
    j=j+i
  end do
  if(mod(presum+A(i),2)/=0)then
    B(i)=1
    C=[i,c]
  endif
end do
print"(I0)",size(c)
do i=1,size(c)
  if(i==1)then
  write(*,'(i0)', advance='no')c(i)
  else
  write(*,'(x,i0)', advance='no')c(i)
  endif
end do
end