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 init() {
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.ParseInt(sc.Text(), 10, 64)
	if e != nil {
		panic(e)
	}
	return int(i)
}

func main() {
	n := nextInt()
	as := make([]int, n+1)
	nn := make([]int, 0, n)

	for i := 1; i <= n; i++ {
		as[i] = nextInt()
	}

	cache := map[int]int{}

	for i := n; i > 0; i-- {
		if v, ok := cache[i]; ok {
			if v%2 == as[i] {
				continue
			}
			if as[i] == 1 && v%2 == 0 {
				nn = append(nn, i)
			}
		} else {
			if as[i] == 1 {
				nn = append(nn, i)
				divs := Divisors(i)
				for _, item := range divs {
					cache[item]++
				}
			}
		}

	}

	l := len(nn)
	fmt.Printf("%#v\n", l)
	if l > 0 {
		// for i := l - 1; i >= 0; i-- {
		// 	fmt.Printf("%#v ", nn[i])
		// }
		for _, item := range nn {
			fmt.Printf("%#v ", item)
		}
		fmt.Println()
	}
}

func Divisors(n int) []int {
	divisors := make([]int, 0, 1000)
	end := int(math.Pow(float64(n), 0.5) + 1)
	for i := 1; i < end; i++ {
		if n%i == 0 {
			divisors = append(divisors, i)
			if v := n / i; i != n/i {
				divisors = append(divisors, v)
			}
		}

	}
	return divisors
}