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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using static System.Console;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        solve();
    }
    static int N;
    static int[] A;
    static void input()
    {
        N = int.Parse(ReadLine());
        A = new int[N + 1];
        int[] tmp = ReadLineParseIntArray();
        for(int i = 0; i < N; i++)
        {
            A[i + 1] = tmp[i];
        }
    }
    static void solve()
    {
        input();
        int[] ans = new int[N + 1];
        int ballCount = 0;
        for(int i = N; i >= 1; i--)
        {
            int c = 0;
            if (2 * i <= N)
            {
                for (int j = 2 * i; j <= N; j += i)
                {
                    c += ans[j];
                }
            }
            ans[i] = (c + A[i]) % 2;
            if (ans[i] == 1)
                ballCount++;
        }
        WriteLine(ballCount);
        int k = 1;
        for(; k < N; k++)
        {
            if (ans[k] == 1)
            {
                Write(k);
                k++;
                break;
                
            }      
        }
        for(; k <= N; k++)
        {
            if (ans[k] == 1)
                Write(" " + k);
        }
        WriteLine();
    }
    static int ReadLineParseInt() => int.Parse(ReadLine());
    static int[] ReadLineParseIntArray() => ReadLine().Split(' ').Select(int.Parse).ToArray();
}