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;

class Program
{
    static int N;
    static void Main()
    {
        N = Int32.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split(' ').Select(x=>Int32.Parse(x)).ToArray();
        var ball = new int[N];

        for (int i=N-1;0<=i;--i)
        {
            var other = (calc(ball, i + 1)) % 2;
            ball[i] = other == 0 ? a[i] : a[i] == 0 ? 1 : 0 ;
        }

        var b = ball.Where(x => x == 1).ToArray();
        var count = b.Count();
        if (count == 0)
        {
            Console.WriteLine(0);
            return;
        }
        Console.WriteLine(count);
        var c = 0;
        for (int i=0;i<N;++i) {
            if (ball[i] == 1)
            {
                Console.Write(i+1);
                c++;
            }
            if (c!=count)Console.Write(" ");
        }
        Console.WriteLine();
    }

    static int calc(int[] ball,int num)
    {
        var index = num;
        var n = 0;
        for (int i=2; ;++i)
        {
            if (N < index*i) break;
            n += ball[index*i - 1];
        }
        return n;
    }
}