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.Collections.Generic;
using System.Linq;



namespace CSharpSample01
{

    
    class Program
    {
        
        static void Solve(int[] a)
        {
            int N = a.Length - 1;
            //b[i] := i番目の箱に入っているボールの数(1 or 0)(i:1～N)
            int[] b = new int[N + 1];
            //ボールが1つ入っている箱の数
            int M = 0;

            //各i番目の箱に対してb[i]を決める
            for(int i = N; i >= 1; i--)
            {
                //iの倍数のインデックスにおいて1をカウント
                int one_cnt = 0;
                for(int j = i; j <= N; j += i)
                {
                    if (b[j] == 1) one_cnt++;
                }

                //one_cntに基づいてb[i]を決める
                if(a[i] == 0)
                {
                    if (one_cnt % 2 == 0) b[i] = 0;
                    else b[i] = 1;
                }
                else
                {
                    if (one_cnt % 2 == 0) b[i] = 1;
                    else b[i] = 0;
                }

                //i番目の箱にボールが入っているならMをインクリメント
                if (b[i] == 1) M++;
            }

            //出力
            Console.WriteLine(M);
            string ans = "";
            //ボールが入っていたらそのインデックス番号を入れる
            for(int i = 1; i <= N; i++)
            {
                if (b[i] == 1) ans = ans + i.ToString();
            }
      
            //M = 0の時表示するものはない
            if(M != 0) Console.WriteLine(string.Join(" ", ans));

        }

        
        static void Main(string[] args)
        {
            //入力1(N)
            int N = int.Parse(Console.ReadLine());

            //入力2(a)
            string[] input = Console.ReadLine().Split(' ');
            int[] a = new int[N + 1];
            for(int i = 1; i <= N; i++)
            {
                a[i] = int.Parse(input[i - 1]);
            }

            Solve(a);
            
        }
    }

}