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>

int main(void)
{
	int N,i;
	scanf("%d",&N);
	int K = N;
	int a[N+1],b[N+1],c[N+1];
	for(i = 1; i <= N; i++)
	{
		c[i] = 0;
	}
	int M=0;
	int d[N];
	for(i = 1; i <= N; i++)
	{
		scanf("%d",&a[i]);
	}
	int count = 1;
	int w,sum;
	int n;
	while(N != 1)
	{
		w = N % 2;
		for(i = N; i > N/2; i--)
		{
			sum = 0;
			count = 1;
			for(n = i; n <= K; n = count*i)
			{
				sum = sum + c[n];
				count++;
			}
			if(a[i] == 1 && sum % 2 == 0)
			{
				c[i] = 1;
				M++;
			}
			else if(a[i] == 0 && sum % 2 == 1)
			{
				c[i] = 1;
				M++;
			}
		}
		N = N /2;
	}
	sum = 0;
	for(i = 2; i <= N; i++)
	{
		sum = sum + c[i];
	}
	if(a[1] == 1 && sum % 2 == 0)
	{
		c[1] = 1;
		M++;
	}
	else if(a[1] == 0 && sum % 2 == 1)
	{
		c[1] = 1;
		M++;
	}
	printf("%d\n",M);
	for(i = 1; i  <= N; i++)
	{
		if(c[i] == 1)
		{
			printf("%d ",i);
		}
	}
	return 0;
}