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.io.PrintStream;
import java.util.Scanner;

public class Main {
    static final Scanner     sc = new Scanner(System.in);
    static final PrintStream so = System.out;

    public static void main(String[] args) {
        int N = nint();
        int[] a = nints(N, 1, 0);
        int[] ball = new int[N+1];
        int r = N; 
        int l = (r+1)/2;
        while(true) {
            for (int i_r = r; i_r >= l; i_r--) {
                ball[i_r] = a[i_r];
                update(a, ball, i_r);
            }
            r = l - 1;
            l = l/2;
            if (r <= 0) break;
        }
        
        
        int m = 0;
        for (int i = 1; i <= N; i++)
            if (ball[i] == 1)
                m++;
        
        so.println(m);
        for (int i = 1; i <= N; i++)
            if (ball[i] == 1)
                so.println(i);
            
    }
    
    private static void update(int[] a, int[] ball, int curr) {
        if (curr == 1) return;
        
        for (int i = 1; i <= Math.sqrt(curr); i++) {
            if (curr % i == 0) {
                a[i] = (a[i] + ball[curr]) % 2;
            }
        }
    }

    private static long nlong() {
        return sc.nextLong();
    }

    private static int nint() {
        return sc.nextInt();
    }

    private static String nstr() {
        return sc.next();
    }

    private static char[] nsToChars() {
        return sc.next().toCharArray();
    }

    private static long[] nlongs(int n) {
        return nlongs(n, 0, 0);
    }

    private static int[] nints(int n) {
        return nints(n, 0, 0);
    }

    private static int[] nints(int n, int padL, int padR) {
        int[] a = new int[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nint();
        return a;
    }

    private static long[] nlongs(int n, int padL, int padR) {
        long[] a = new long[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nlong();
        return a;
    }

    private static String[] nstrs(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = nstr();
        return a;
    }

    private static char[][] nsToChars2D(int h, int w) {
        return nsToChars2D(h, w, 0);
    }

    private static char[][] nsToChars2D(int h, int w, int pad) {
        char[][] a2 = new char[h + pad * 2][w + pad * 2];
        for (int i = 0; i < h; i++)
            System.arraycopy(nsToChars(), 0, a2[pad + i], pad, w);
        return a2;
    }
}