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: Runtime Error)

#include<stdio.h>

int main(){
    int a, b, flag, n, i, j, count;
    flag = 0;
    count = 0;
    int A[200001];
    int B[200001];
    scanf("%d", &n);
    for(i = 0; i < n; i++){
        scanf("%d", &A[i]);
    }
    for(i = n-1; i >= 0; i--){
        b = 0;
        if(n/(i+1) == 1){
            B[i] = A[i];
            if(A[i] == 1)count++;
        }else{
            a = n/(i+1);
            if(i == 0){
                if(A[i] == 0)B[i] = (count%2 + A[i])%2;
                break;
            }
            for(j = 2; j <= a+1; j++){
                b += B[((i+1)*j)-1];
            }
            if(b%2 == 0 && A[i] == 0){B[i] = 0;}
            if(b%2 == 0 && A[i] == 1){B[i] = 1;count++;}
            if(b%2 == 1 && A[i] == 0){B[i] = 1;count++;}
            if(b%2 == 1 && A[i] == 1){B[i] = 0;}
        }
        
    }
    if(count == 0){
        printf("0\n");
    }else{
        printf("%d\n", count);
        for(i = 0; i < n; i++){
            if(B[i] == 1){
            printf("%d ", i+1);
            }
        }
        printf("\n");
    }
    return 0;
}