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"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func scanNums(len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		num = nextInt()
		nums = append(nums, num)
	}
	return
}

func refbit(i int, b int) int {
	return (i >> uint8(b)) & 1
}

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()
	a := scanNums(n)
	patternNum := int(math.Pow(2, float64(n)))
	count := 0
	correctCount := 0
	correctBox := make([]bool, n)
	for i := 0; i < patternNum; i++ {
		box := make([]bool, n)
		count = 0
		for j := 0; j < n; j++ {
			if refbit(i, j) == 1 {
				box[j] = true
			} else {
				box[j] = false
			}
		}
		for j := 0; j < n; j++ {
			sum := 0
			for k := 0; k < n; k++ {
				if (k+1)%(j+1) == 0 {
					if box[k] == true {
						sum++
					}
				}
			}
			if sum%2 == a[j] {
				count++
			}
		}
		if count == n {

			correctCount++
			correctBox = box
		}
	}

	if correctCount == 1 {
		falseCount := 0
		for i := 0; i < n; i++ {
			if correctBox[i] == false {
				falseCount++
			}
		}
		if falseCount == n {
			fmt.Println(0)
			return
		}
	}

	if correctCount > 0 {
		fmt.Println(correctCount)
		num := 0
		for i := 0; i < n; i++ {
			if correctBox[i] {
				if num > 0 {
					fmt.Print(" ")
				}
				fmt.Print(i + 1)
				num++
			}
		}
		fmt.Println()
	} else {
		fmt.Println(-1)
	}
}