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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"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 nextLine() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = nextInt()
	}
	b := make([]int, n)

	for i := n; i >= 1; i-- {
		// iの倍数の箱に入ってるボールの数の合計
		sum := 0
		for j := i + i; j <= n; j += i {
			sum ^= b[j-1]
		}
		b[i-1] = sum ^ a[i-1]

	}

	ans := make([]int, 0, len(a))
	for i, e := range b {
		if e == 1 {
			ans = append(ans, i+1)
		}
	}

	fmt.Println(len(ans))
	if len(ans) != 0 {
		for _, a := range ans {
			fmt.Printf("%d ", a)
		}
		fmt.Println()

	}

}

// func main() {
// 	sc.Split(bufio.ScanWords)

// 	n := nextInt()
// 	a := make([]int, n)
// 	b := make([]int, n+1)
// 	for i := 0; i < n; i++ {
// 		a[i] = nextInt()
// 	}

// 	m := map[int]int{}
// 	for i := 1; i <= n; i++ {
// 		m[i] = n / i
// 	}

// 	for i := n; i >= 1; i-- {
// 		if m[i] == 1 {
// 			b[i] = 1
// 			continue
// 		} else {
// 			b[i] = 0
// 			continue
// 		}

// 	}

// }