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: Accepted)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int[] ARRAY = new int[N];

        for (int i = 0; i < N; i++) {
            ARRAY[i] = scanner.nextInt();
        }

        int[] ballArray = new int[N];
        for (int i = N; i > 0; i--) {
            int bairitu = 2;
            int count= 0;
            while ((i * bairitu) <= N) {
                if (ballArray[i * bairitu - 1] == 1) {
                    count++;
                }
                bairitu++;
            }

            if (ARRAY[i-1] == 1) {
                if (count % 2 == 0) {
                    ballArray[i-1] = 1;
                }
            } else {
                if (count % 2 == 1) {
                    ballArray[i-1] = 1;
                }
            }
        }

        List<Integer> resultList = new ArrayList<>();
        for (int i=0; i<N; i++) {
            if (ballArray[i] == 1) {
                resultList.add(i+1);
            }
        }

        StringBuilder sb = new StringBuilder();
        System.out.println(resultList.size());
        for (Integer result : resultList) {
            sb.append(result).append(" ");
        }
        System.out.println(sb.toString());
    }
}