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: Accepted)

program main
  implicit none
  integer i,N,i2,ball,j,t
  integer,allocatable :: a(:),b(:),b2(:)
  !read(*, *) (L(i), i = 1,N)
  read(*, *) N
  allocate(a(N))
  allocate(b(N))
  allocate(b2(N))
  read(*, *) (a(i), i = 1,N)
  b2 = a
  t = 1
  do i = 1,N
    i2 = N-i+1
    ball = 0
    do j = 1,N/i2
      ball = ball+b2(i2*j)
    end do
    !b(i2) = mod(ball,2)
    ball = mod(ball,2)
    b2(i2) = ball
    if (ball == 1) then
      b(t) = i2
      t = t+1
    end if
  end do
  write(*, *) t-1
  if (t /= 1) then
    write(*, *) b(1:t-1)
  end if
end program main