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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws Exception {
		// TODO 自動生成されたメソッド・スタブ
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String W = in.readLine();
		int N = Integer.parseInt(W);

		int[] A = new int[N+1];
		A[0]=0;
		W = in.readLine();
		String[] Ws = W.split(" ");
		for(int i=1;i<N+1;i++){
			A[i]=Integer.parseInt(Ws[i-1]);
		}

		int[] B = new int[N+1];
		long ans = 0;
		long p = 1;
		for(int i=1;i<N+1;i++){
			int x =0;
			for(int k = i;k<N+1 ;k=k+i){
				x+=A[k];
			}
			ans+=(p*(x%2));
			p=p<<1;
		}

		System.out.println(ans);
	}

}