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.Linq;
using System.Collections.Generic;

namespace ABC134
{
    class D
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var res = new int[N];

            // for i (0,N)
            // aiの倍数となる値のたまの数を合計する
            // 奇数か偶数家判定する。
            // aiが1&&合計が奇数なら入れない。aiが1&&合計が偶数なら入れる
            // aiが0&&合計が奇数なら入れる。aiが0&&合計が偶数なら入れない

            for (int i = N - 1; i >= 0; i--)
            {
                var ballsum = 0;
                var isum = i + 1;
                while (isum + (i + 1) <= N)
                {
                    isum += (i + 1);
                    if (res[a[isum - 1]] == 1) ballsum++;
                }

                if (a[i] == 1)
                {
                    if (ballsum % 2 == 0) res[i]++;
                }
                else
                {
                    if (ballsum % 2 == 1) res[i]++;
                }
            }

            Console.WriteLine(res.Count(x => x == 1));
            var index = 0;
            foreach (var i in res)
            {
                index++;
                if (i != 0)
                {
                    Console.Write(index);
                    if (index != N) Console.Write(" ");
                }
            }

            Console.WriteLine();

        }
    }
}