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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

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

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Long> aList = new ArrayList();
        for (int i = 1; i <= n; i++) {
            aList.add(sc.nextLong());
        }

        List<Long> resultList = new ArrayList();
        boolean minusFlg = false;
        for(int i = n - 1; i>=0; i--) {
            if (i % 2 == 0) {
                long temp = i + 1;

                List<Long> tempAList = resultList.stream().filter(r -> r % temp == 0).collect(Collectors.toList());
                long tempSum = 0L;
                for(long t: tempAList) {
                    tempSum += t;
                }
                if (aList.get(i) == 0) {
                    if (tempSum % 2L != 0l) {
                        resultList.add(temp);
                    };
                } else {
                    if (tempSum % 2L == 0l) {
                        resultList.add(temp);
                    };
                }
            } else {
                if(aList.get(i) == 1) {
                    minusFlg = true;
                    break;
                }
            }
        }
        if(minusFlg) {
            System.out.print(-1);
        } else if (resultList.isEmpty()) {
            System.out.print(0);
        } else {
            resultList.stream().sorted().forEach(r-> System.out.print(r + " "));
        }
    }
}