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;

namespace abc134_d
{
    static class Program
    {
        static void Main(string[] args)
        {
            var n = Console.ReadLine().ToInteger();
            var a = Console.ReadLine().ToIntArray();

            // 偶数か奇数かなので、ボールを1つ入れるか入れないかだけを考えればいい。

            var boxes = new int[n];
            for (int i = 0; i < a.Length; i++)
            {
                // 逆さから考える。
                var number = a.Length - i;
                var index = number - 1;
                if (number > n / 2)
                {
                    // 後ろ半分は、倍数は他に存在しないので、確定。
                    boxes[index] = a[index];
                }
                else
                {
                    // 倍数がいくつあるか
                    var div = n / number - 1;
                    // 倍数の総和
                    var sum = 0;
                    for (int j = 0; j < div; j++)
                    {
                        sum += boxes[number * (j + 2) - 1];
                    }
                    if (sum % 2 != a[index])
                    {
                        // 総和が条件に一致しないときだけ1を足す
                        boxes[index] = 1;
                    }
                }
            }
            Console.WriteLine($"{boxes.Where(m => m > 0).Count()}");
            Console.WriteLine($"{string.Join(" ", boxes.Select((m, i) => m > 0 ? (i + 1).ToString() : ""))}");
        }

        static int ToInteger(this string s)
        {
            return int.Parse(s);
        }

        static int[] ToIntArray(this string s, char separator = ' ')
        {
            return s.Split(separator).Select(m => m.ToInteger()).ToArray();
        }
    }
}