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;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int[]A = new int[N];
		string[] str = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str[i]);
		}
		int[]B = new int[N];
		int[]C = new int[N];
		var list = new List<int>();
		for(var i=N-1;i>=0;i--){
			if((i+1)*2>N){
				if(A[i]==1){
					list.Add(i+1);
					B[i]=1;
					C[i]=1;
				}
			} else {
              	int a1 = 0;
              	if((i+1)*2-1<N){
                  a1 = C[(i+1)*2-1];
                }
              	int a2 = 0;
              	if((i+1)*3-1<N){
                  a2 = C[(i+1)*3-1];
                }
                 int a3 = 0;
              	if((i+1)*6-1<N){
                  a3 = C[(i+1)*6-1];
                }
				if((A[i]+a1+a2+a3)%2==1){
					list.Add(i+1);
					B[i]=1;
					C[i]=1;
				}
			}
		}
      	list.Sort();
		Console.WriteLine(list.Count);
		if(list.Count>0){
			Console.Write(list[0]);
		for(var i=1;i<list.Count;i++){
			Console.Write(" "+list[i]);
		}
		}
	}
}