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 extends App {

  import scala.collection.mutable

  val n = scala.io.StdIn.readLine.toInt
  val a = scala.io.StdIn.readLine.split(" ").map(_.toInt)

  var data = mutable.TreeSet.empty[Int]

  var cnt = n

  def getOdd(cnt: Int): Boolean = {
    data.count { a => a % cnt == 0 } % 2 == 0
  }

  def getOdd2(cnt: Int): Boolean = {
    var sumcnt = 0
    var now = cnt + cnt
    while (now <= n) {
      if (data(now)) {
        sumcnt += 1
      }

      now += cnt
    }

    sumcnt % 2 == 0
  }

  while (cnt >= 1) {
    val array_cnt = cnt - 1
    // 偶数 or 奇数
    val odd = getOdd2(cnt)

    if (odd && a(array_cnt) == 0) {
      // 偶数 & 求めるのも偶数
      //何もしない
    } else if (odd && a(array_cnt) == 1) {
      // 偶数 & 求めるのは奇数
      data += cnt
    } else if (!odd && a(array_cnt) == 0) {
      // 奇数 & 求めるのは偶数
      data += cnt
    } else if (!odd && a(array_cnt) == 1) {
      // 奇数 & 求めるのは奇数
      // なにもしない
    }
    cnt -= 1
  }

  println(data.size)
  if (data.nonEmpty) {
    println(data.toList.sorted.mkString(" "))
  }
}