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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <malloc.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>

//abc135D
int main(void) {
  int n, k, i, r, d, cou=0, tmp, len, m=0, max=0, premax=0;
  scanf("%d", &n);
  int a[n], b[n];

  for(i=0; i < n; i++){
    scanf("%d", &a[i]);
    b[i]=0;
  }

  for(i=n - 1; i >= 0; i--){
    cou=0;
    while((i + 1) * (cou + 2) <= n){
      //printf("b[%d]=%d=(%d+%d)%%2\n",i, (b[i] + b[(i + 1) * (cou + 2) - 1])%2,b[i], b[(i + 1) * (cou + 2) - 1]);
      b[i]=(b[i] + b[(i + 1) * (cou + 2) - 1])%2;
      //printf("b[%d]=%d\n\n",i,tmp);
      cou++;
    }
    //printf("bef  a[%d]=%d   b[%d]=%d\n", i, a[i], i, b[i]);
    b[i]=(b[i] + a[i])%2;
    //printf("aft  a[%d]=%d   b[%d]=%d\n\n", i, a[i], i, b[i]);
    if(b[i] == 1) m++;
  }

  printf("%d\n", m);
  for(i=0; i < n; i++){
    if(b[i] == 1) printf("%d ", i + 1);
  }
  return 0;
}