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: Wrong Answer)

#include <stdio.h>
#include <string.h>
#define MAX_N 200001

int main(void) {
  int N;
  scanf("%d", &N);
  int A[MAX_N];
  for(int i = 1; i <= N; i++) {
    scanf("%d", &A[i]);
  }

  int B[MAX_N];
  memset(B, 0, sizeof(int)*N);
  for(int i = 1; i <= N/2; i++) {
    for(int j = 1; j <= N; j++) {
      int x = i * j;
      if(x > N) break;
      if(A[i])
	B[x]++;
    }
  }

  int M = 0;
  for(int i = 1; i <= N/2; i++) {
    if(A[i] != (B[i] % 2)) {
      printf("-1\n");
      return 0;
    }
    if(B[i] % 2)
      M++;
  }

  printf("%d\n", M);
  for(int i = 1; i <= N / 2; i++) {
    if(B[i])
      printf("%d ", i);
  }
  for(int i = (N+1) / 2; i <= N; i++) {
    if(A[i])
      printf("%d ", i);
  }
  printf("\n");
  
  return 0;
}