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.Linq;

class Program
{
    static void Main(string[] args) {
        String ret;
        ret = process(new System.IO.StreamReader(Console.OpenStandardInput()));
        //ret = process("5\n0 0 0 0 0");

        Console.WriteLine(ret);
        //Console.ReadLine();
    }

    static string process(System.IO.TextReader input) {
        int n     = int.Parse(input.ReadLine());
        int[] ary = ToIntArray(input.ReadLine(), n);

        int[] ans = new int[n];

        for(int i=n; i>=1;  i--) {
            int k = 2;
            int ball = ary[idx(i)];
            while(true) {
                if(idx(i*k) > idx(n)) {
                    ans[idx(i)] = ball % 2;
                    break;
                } else {
                    ball += ary[idx(i*k)];
                    k += 1;
                }
            }
        }

        int count = ans.Count(x => x == 1);
        
        StringBuilder ret = new StringBuilder();
        ret.AppendLine(count.ToString());
        for (int i=0; i<n; i++) {
            if (ans[i] == 1) {
                ret.Append(i+1);
                ret.Append(' ');
            }
        }

        return ret.ToString();
    }
    static int idx(int n) {
        return n - 1;
    }

    static string process(string input) {
        return process(new System.IO.StringReader(input));
    }

    static int[] ToIntArray(string strs, int n) {
        int[] ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++) ret[i] = int.Parse(spl[i]);
        return ret;
    }
}