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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

const maxn = trunc(2e5);
var a,b:array[1..maxn] of longint;
    n,m,s,i,j:longint;
    check:boolean;

begin
	readln(n); 
	for i:=1 to n do read(a[i]);
	m:=0; check:=true;
	for i:=1 to n do
	  begin
	    s:=a[i];
	    j:= 2 * i;
	    while j<=n do
	      begin
	        s:=s + a[j];
	        j:=j +i;
	      end;
	    if (s mod 2 = a[i]) and (a[i] = 1) then 
	      begin
	        inc(m); b[m]:=i;
	      end;
	    if s mod 2 <> a[i] then check:=false;
	    if not check then break;
	  end;
	if not check then write(-1)
	else 
	  begin
    	writeln(m);
    	for i:=1 to m do write(b[i],' ');
    end;
end.