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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	buffer := make([]byte, 200000)
	scanner.Buffer(buffer, 10*200000)
	var n int
	scanner.Scan()
	n, _ = strconv.Atoi(scanner.Text())
	a := make([]int, n)
	scanner.Scan()
	args := strings.Split(scanner.Text(), " ")
	for i := 0; i < n; i++ {
		var j int
		j, _ = strconv.Atoi(args[i])
		a[i] = j
	}

	b := make([]int, n)
	for i := n - 1; i >= 0; i-- {
		j := (i + 1) * 2
		if j > n {
			b[i] = a[i]
		} else {
			if b[j-1]%2 == 0 {
				b[i] = b[j-1] + a[i]
			} else {
				b[i] = b[j-1] + (a[i]+1)%2
			}
		}
	}

	ans := make([]string, n)
	m := 0
	for i := 0; i < n; i++ {
		if b[i]%2 == 1 {
			ans[m] = fmt.Sprint(i + 1)
			m++
		}
	}

	buf := strings.Join(ans, " ")

	fmt.Println(m)
	if m != 0 {
		fmt.Println(buf)
	}
}