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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace cs
{
    public class Program
    {
        public static void Main(string[] args)
        {


            
            var N = int.Parse(Console.ReadLine());

            var ball = new int[N+1];
            var currentLine = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            currentLine[1] = int.MinValue;
            var currentMin = int.MaxValue;
            bool cnt = false;
            int x = 0;
            int total = 0;


            for(int i = N; i > 0; i--){
                cnt = false;
                x = 2;
                while(x * i <= N){
                    if(ball[x * i] == 1){
                        if(cnt) cnt = false;
                        else cnt = true;
                    }
                    x++;
                }

                if(currentLine[i-1] == 1){
                    if(cnt) ball[i] = 0;
                    else {
                        ball[i] = 1;
                        total++;
                    }
                }else{
                    if(cnt) {
                        ball[i] = 1;
                        total++;
                    }
                    else ball[i] = 0;
                }
            }

            Console.WriteLine(total);
            foreach(var tgt in ball){
                if(tgt == 1){
                    Console.Write(tgt);
                    if(total != 1){
                        Console.Write(" ");
                        total--;
                    }
                }
            }



            //Console.ReadKey();
           
        }


        public static long modder(){
            return (long)Math.Pow(10,9) + 7;
        }

        public static long GCD(long n, long m){
            
            if(m % n == 0) return n;
            else return GCD(m%n, n);

        }

        public static long LCD(long n, long m){

            return m * n / GCD(n,m);
        }
    }
}