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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>

int main(void){

	int n;
	int a[200001];
	int i,j;
	int buff;
	int count;

	scanf("%d",&n);

	for(i=0;i<n;i++){
		scanf("%d",&a[i+1]);
	}
	count = 0;
	for(i=int(double(n)/2+0.5);i<n;i++){
		if(a[i] == 1){
			count++;
		}
	}

	for(i=n/2;i>0;i--){
		//i*2の倍数の合計を取得
		buff = a[i*2];

		for(j=i+i*2;n+1>j;j+=i*2){
			buff += a[j];
		}

		if(buff%2 != a[i]){
			count++;
		}
	}

	printf("%d\n",count);

	for(i=int(double(n)/2+0.5);i<n;i++){
		if(a[i] == 1){
			printf("%d ",i);
		}
	}

	for(i=n/2;i>=0;i--){
		//i*2の倍数の合計を取得
		buff = a[i*2];

		for(j=i+i*2;n+1>j;j+=i*2){
			buff += a[j];
		}

		if(buff%2 == a[i]){
		}else{
			printf("%d ",i);
		}
	}


				
	printf("\n");


	return 0;
}