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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int n;
  cin>>n;
  int a[n];
  for(int i=0; i<n; i++) cin>>a[i];

  bool ans[n];
  for(int i=0; i<n; i++) ans[i]=false;

  for(int i=n; i>=1; i--) {
    if(n<2*i) ans[i-1] = a[i-1];
    else {
      int count = 0;
      int tmp = 2;
      while(i*tmp<=n) {
        if(ans[i*tmp-1]) count++;
        tmp++;
      }
      count += a[i-1];
      ans[i-1] = count%2;
    }
  }

  int sum = 0;
  for(int i=0; i<n; i++) {
    if(ans[i]) sum++;
  }

  cout<<sum<<endl;

  int cnt = 0;
  for(int i=0; i<n; i++) {

    if(ans[i]) {
      cnt++;
      if(cnt==sum) cout<<i+1<<endl;
      else cout<<i+1<<' ';
    }
  }

  return 0;
}