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"
)

func nextInt(sc *bufio.Scanner) int {
	sc.Scan()
	t, _ := strconv.Atoi(sc.Text())
	return t
}

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n+1)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	for i := 1; i <= n; i++ { // 1-indexed
		a[i] = nextInt(sc)
	}
	box := make([]int, n+1)
	for i := n; i >= 1; i-- { // 大きい方から(Nから降順に)見ていく
		sum := 0
		for j := i; j <= n; j += i { // i<=nの間にiの倍数は何個あるか？
			sum += box[j] // iの倍数に対応する箱に入っているボールの数を追跡する
		}
		// fmt.Println("sum[", i, "]", sum, "a[", i, "]=", a[i])
		if (a[i] == 1 && sum%2 == 0) ||
			(a[i] == 0 && sum%2 == 1) {
			box[i]++
		}
	}
	ans := 0
	for i := 1; i < len(box); i++ {
		if box[i] == 1 {
			ans++
		}
	}
	fmt.Println(ans)
	for i := 1; i <= ans; i++ {
		fmt.Print(box[i], " ")
	}
	if ans > 0 {
		fmt.Println()
	}
}