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.util.Scanner;
import java.util.HashMap;
import java.util.List;
import java.util.Arrays;
import java.util.ArrayList;
import java.lang.Math;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            if (i >= n / 2) {
                int tmp = a[i];
                b[i] = tmp;
            }
        }
        for (int i = n/2-1; i >= 0; i--) {
            int sum = 0;
            for (int j = 2; j <= n/(i+1); j++) {
                sum += b[(i+1)*j-1];
            }
            if (a[i] == 0) {
                if (sum % 2 == 0) {
                    b[i] = 0;
                } else {
                    b[i] = 1;
                }
            } else {
                if (sum % 2 == 0) {
                    b[i] = 1;
                } else {
                    b[i] = 0;
                }
            }
        }
        boolean flag = true;
        for (int i = 0; i < n; i++) {
            if (a[i] != b[i]) {
                flag = false;
            }
        }
        if (flag) {
            System.out.println("-1");
        } else {
            int ans = 0;
            ArrayList<Integer> ansans = new ArrayList<Integer>();
            for (int i = 0; i < n; i++) {
                if (b[i] == 1) {
                    ans++;
                    ansans.add(i+1);
                }
            }
            System.out.println(ans);
            for (int i = 0; i < ansans.size(); i++) {
                if (i == ansans.size()-1) {
                    System.out.println(ansans.get(i));
                } else {
                    System.out.print(ansans.get(i) + " ");
                }
            }
        }
    }

}