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.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming
{
  public void Solve()
  {
    var N = Int1;
    var a = Ints;
    var ans = new int[N];
    for (int i = N; i > 0; --i)
    {
      int j = 0;
      int sum = 0;
      while (true)
      {
        j += i;
        if (j > N) break;
        sum += ans[j - 1];
      }
      if ((sum % 2) != (a[i - 1] % 2)) ans[i - 1] = 1;
    }
    int k = ans.Where(l => l == 1).Sum();
    var wr = new List<int>();
    for (int i = 0; i < N; ++i)
    {
      if (ans[i] == 1)
        wr.Add(i + 1);
    }
    Write(k);
    if (k > 0) Write(wr.ToArray());
  }
}


public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long i, long N, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (N > 0)
    {
      if ((N & 1) != 0) res = res * i % MOD;
      i = i * i % MOD;
      N >>= 1;
    }
    return res;
  }
  public static long Power2(long i, long N)//i^N
  {
    long res = 1;
    while (N > 0)
    {
      if ((N & 1) != 0) res = res * i;
      i = i * i;
      N >>= 1;
    }
    return res;
  }
  public static long GCD(long i, long N)
  {
    if (i > N) Swap(ref i, ref N);
    if (i == 0) return N;
    while (N != 0)
    {
      var r = i % N;
      i = N;
      N = r;
    }
    return i;
  }
  public static long LCM(long i, long N) => i * N / GCD(i, N);
  public static long Comb(long N, long R, int MOD = 1000000007)
  {
    long ret = 1;
    long x = 1;
    for (long i = N; i >= N - R + 1; --i)
    {
      ret = ret / x * i;
      ret %= MOD;
      x++;
    }
    return ret;
  }
  public static long Comb2(long N, long R)
  {
    long Nume = 1;
    long Deno = 1;

    if (R > N - R) R = N - R;
    for (long i = 1; i <= R; ++i)
    {
      Deno *= i;
      Nume *= N - i + 1;
    }
    return Nume / Deno;
  }

}
public static class Utils
{

  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(int N)
  {
    string s = N.ToString();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Write(string a) => Console.WriteLine(a);
  public static void Write(params object[] i) => Write(string.Join(" ", i));
  public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
  public static void Verticalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
  public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }
}