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)

/* ABC133-C.c
   Takatan */

#include<stdio.h>
#include<stdlib.h>
int main(void){
    int number, *array, count, check, i, j;
    count = 0;

    scanf( "%d" , &number);
    array = malloc(sizeof(int) * (number+1));
    for(i=0; i < number; i++){
        scanf( "%d" , array+i+1);
    }

    for(i=number; i > 0; i--){
        if(array[i]){
            check = 1;
            count += 1;

            for(j=2; j <= number/i; j++){
                check += array[i*j];
            }
            if(check!=1){
                array[i] = 0;
                count -= 1;
            }
        }
        check = 0;
        for(j=1; j <= number/i; j++){
            check += array[i*j];
        }
        if(array[i]!=check){
            printf( "-1\n" );
            return 0;
        }
    }

    printf( "%d" , count);
    check = 0;
    for(i = 1; i <= number; i++){
        if(array[i]){
            if(check){
                printf( " %d" , i);
            }else{
                printf( "\n%d" , i);
                check = 1;
            }
        }
    }
    printf( "\n" );
    return 0;
}