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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
public class ABC134D {
    public static void Main() {
        int N, M = 0, sum = 0;
        string ans = "";
        List<int> a = new List<int>(), b = new List<int>();
        N = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        for (int i = 0; i < N; i++) {
            a.Add(int.Parse(str[i]));
            b.Add(0);
        }
        for (int i = N - 1; i >= 0; i--) {
            sum = 0;
            for (int j = 2; j * (i+1) <= N; j++) {
                sum += b[j * (i+1) - 1];
            }
            sum %= 2;
            if (sum == a[i]) b[i] = 0;
            else {
                b[i] = 1;
                M++;
            }
        }
        Console.WriteLine(M);
        for (int i = 0; i < N; i++) {
            if (b[i] == 1) {
                if (ans == "") ans += (i + 1).ToString();
                else ans += " " + (i + 1).ToString();
            }
        }
        if (ans != "") Console.WriteLine(ans);
    }
}