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.*;

public class Main {
    static long mod = 1000000007;

    public static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        } else if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n+1];
        int[] r = new int[n+1];

        for (int i = 1; i <= n; ++i) {
            a[i] = sc.nextInt();
        }

        for (int i = n; i >= 1; --i) {
            int total = 0;
            for (int j = i * 2; j <= n; j += i) {
                total += r[j];
            }
            if (total % 2 == a[i]) {
                r[i] = 0;
            } else {
                r[i] = 1;
            }
        }

        int cnt = 0;
        for (int i = 1; i <= n; ++i) {
            // System.err.println(String.format(">> %d %d", i, r[i]));
            if (r[i] > 0) {
                cnt++;
            }
        }

        System.out.println(cnt);
        if (cnt > 0) {
            StringBuilder sb = new StringBuilder();
            for (int i = 1; i <= n; ++i) {
                if (r[i] > 0) {
                    sb.append(i);
                    cnt--;
                    if (cnt > 0) {
                        sb.append(" ");
                    }
                }
            }
            System.out.println(sb.toString());
        }
    }
}