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: Time Limit Exceeded)

import java.util.Scanner;

public class Main{

    public static void main(String args[]){

        Scanner scan = new Scanner(System.in);
        Integer n = Integer.parseInt(scan.next());

        Integer a[] = new Integer[n];
        for(int i=0;i<n;i++)
            a[i] = Integer.parseInt(scan.next());

        Integer b[] = new Integer[n];
        for(int i=n-1;i>=0;i--){
            if((i+1) > n/2){
                //System.out.println("X");
                b[i] = a[i];
            }else{
                //System.out.println("Y");
                int tmp = i+1;
                int sum = 0;
                while(true){
                    //System.out.println("YO");
                    if((tmp += (i+1)) <= n){
                        sum += b[tmp-1];
                        //System.out.println(tmp + "  " + sum);
                    }else{
                        break;
                    }
                }
                //System.out.println(i + "  " + sum);
                if(sum%2==a[i])
                    b[i] = 0;
                else
                    b[i] = 1;
            }
        }
        int cnt=0;
        String str = "";
        for(int i=0;i<n;i++){
            if(b[i]==1){
                str += (i+1) + " ";
                cnt++;
            }
        }
        System.out.println(cnt);
        if(cnt != 0)
            System.out.println(str);
    }
}