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 Scala (2.11.7) (judge verdict: Accepted)


object Main {

  def printArray(arr: Array[Int]): Unit =
    println(arr.mkString("\n"))

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)

    // 1以上N以下の任意の整数iについて, iの倍数が書かれた箱に入っている
    // ボールの個数の和を2で割った余りがa_iである

    val N = sc.nextInt()
    val A = Array.fill(N)(sc.nextInt() match {
      case 1 => true
      case 0 => false
    })

    // 言い換えると, 1以上,N以下の任意のiについて
    // iの倍数の個数を2で割った余りがa_iであるかどうか
    val B = new Array[Boolean](N)
    var i = N
    while (i > 0) {
      var s = false
      var j = 2
      while (i * j <= N) {
        s ^= B(i * j - 1)
        j += 1
      }
      if (s != A(i-1))
        B(i-1) = true
      i -= 1
    }
    val boxes = B.zipWithIndex.filter(_._1)
    val M = boxes.length
    val results = boxes.map(_._2 + 1).mkString(" ")
    println(M)
    if (M != 0)
      println(results)
  }

}