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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

class AtCoder
{
    const int MOD = 1000000007;
    public void Slove()
    {
        var n = int.Parse(Console.ReadLine());
        var array = Console.ReadLine().Split().Select(int.Parse).ToArray();

        var ans = new int[array.Length];
        for(int i = array.Length - 1; i >= 0; i--)
        {
            if(array[i] != (ans[i] & 1))
            {
                ans[i]++;
                int v1 = i + 1;
                for(int j = 0; j <= Math.Sqrt(i); j++)
                {
                    int v2 = j + 1;
                    int v3 = v1 / v2;
                    if(v1 == v3 * v2)
                    {
                        ans[j]++;
                        if(v2 != v3)
                            ans[v3 - 1]++;
                    }
                }
            }
        }
        var cnt = ans.Sum(x => x & 1);
        Console.WriteLine(cnt);
        if(cnt > 0)
            Console.WriteLine(string.Join(" ", 
                ans
                .Select((x, index) => new { x, index})
                .Where(item => (item.x & 1) == 1)
                .Select(item => item.index + 1)
                ));
    }
    static void Main()
    {
        var ac = new AtCoder();
        ac.Slove();
    }
}