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"
)

func solve() {
	n := getInt()
	as := getIntSlice(n)

	ans := make([]int, n)
	for i := n; i >= 1; i-- {
		s := 0
		for j := i * 2; j <= n; j += i {
			s += ans[j-1]
		}
		ans[i-1] = ((s % 2) ^ as[i-1])
	}

	fmt.Fprintln(wr, sum(ans...))
	for i, a := range ans {
		if a == 1 {
			fmt.Fprintln(wr, i+1)
		}
	}
}

func sum(ns ...int) int {
	var sum int
	for _, n := range ns {
		sum += n
	}
	return sum
}

// -----------------------------------------

const (
	inf = 1 << 60
	// mod = 1000000007
)

var (
	sc = bufio.NewScanner(os.Stdin)
	wr = bufio.NewWriter(os.Stdout)
)

func main() {
	maxBufSize := int(1e8)
	sc.Buffer(make([]byte, 4096), maxBufSize)
	sc.Split(bufio.ScanWords)
	solve()
	wr.Flush()
}

func getInt() (ret int) {
	sc.Scan()
	ret, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return
}

func getIntSlice(n int) (ret []int) {
	ret = make([]int, n)
	for i := range ret {
		ret[i] = getInt()
	}
	return
}

func getString() (ret string) {
	sc.Scan()
	ret = sc.Text()
	return
}

func getRunes() (ret []rune) {
	ret = []rune(getString())
	return
}