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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;


public class Main {
    int N;
    int[] a;

    private List<Integer> getPrimes(int n) {
        ArrayList<Integer> primes = new ArrayList<>();
        for(int i = 2;i <= n;i++) {
            boolean flag = true;
            for(int j = 2;j * j <= i;j++) {
                if (i % j == 0) {
                    flag = false;
                    break;
                }
            }

            if (flag) {
                primes.add(i);
            }
        }

        return primes;
    }

    private void solve() {
        N = nextInt();
        a = new int[N];
        for(int i= 0;i < N;i++) {
            a[i] = nextInt();
        }

        List<Integer> primes = getPrimes(N);
//        out.println(primes);
        int[] b = new int[N];
        int[] c = new int[N];
        for(int i = N - 1;i >= 0;i--) {
            if (a[i] != (b[i] + c[i]) % 2) {
                b[i]++;

                for (int prime : primes) {
                    int j = i + 1;
                    if (prime >= j) {
                        break;
                    }

                    while (j % prime == 0 && j > 0) {
                        j /= prime;
                        c[j - 1]++;
                        c[j - 1] %= 2;
                    }
                }
                if (i != 0) {
                    c[0]++;
                }
            }
        }

//        out.println(Arrays.toString(a));
//        out.println(Arrays.toString(b));
//        out.println(Arrays.toString(c));
        for(int i = 0;i < N;i++) {
            if (a[i] != (b[i] + c[i]) % 2) {
                out.println(-1);
                return;
            }
        }

        int sum = 0;
        for(int i = 0;i < N;i++) {
            sum += b[i];
        }
        out.println(sum);
        ArrayList<Integer> ans = new ArrayList<>();
        for(int i = 0;i < N;i++) {
            if (b[i] == 1) {
                ans.add(i + 1);
            }
        }

        for(int i = 0;i < ans.size();i++) {
            if (i != 0) {
                out.print(" " + ans.get(i));
            } else {
                out.print(ans.get(i));
            }
        }
        out.println();
    }

    public static void main(String[] args) {
        out.flush();
        new Main().solve();
        out.close();
    }

    /* Input */
    private static final InputStream in = System.in;
    private static final PrintWriter out = new PrintWriter(System.out);
    private final byte[] buffer = new byte[4096];
    private int p = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (p < buflen)
            return true;
        p = 0;
        try {
            buflen = in.read(buffer);
        } catch (IOException e) {
            e.printStackTrace();
        }
        if (buflen <= 0)
            return false;
        return true;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrint(buffer[p])) {
            p++;
        }
        return hasNextByte();
    }

    private boolean isPrint(int ch) {
        if (ch >= '!' && ch <= '~')
            return true;
        return false;
    }

    private int nextByte() {
        if (!hasNextByte())
            return -1;
        return buffer[p++];
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = -1;
        while (isPrint((b = nextByte()))) {
            sb.appendCodePoint(b);
        }
        return sb.toString();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}