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 A319D
    implicit none
    integer(8)::N,calc,i,j,bcount
    integer(8),allocatable,dimension(:)::A,ans
    read*,N
    allocate(A(N))
    allocate(ans(N))
    read*,A
    ans=0
    bcount=0
    do i=0,N-1
        calc=0
        do j=1,N/(N-i)
            calc=calc+ans(j*(N-i))
        end do
        if(A(N-i)==0)then
            if(mod(calc,2)==1)then
                ans(N-i)=1
                bcount=bcount+1
            end if
        else
            if(mod(calc,2)==0)then
                ans(N-i)=1
                bcount=bcount+1
            end if
        end if
    end do

    print'(i0)',bcount
    do i=1,N
        if(ans(i)==1)write(*,fmt='(i0,1x)',advance='no')i
    end do
    print'(A)',""
end program A319D