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 (
	"fmt"
)

func main() {
	var N int
	fmt.Scan(&N)

	input := append([]int{0},scanNums(N)...)
	output := make([]int, N+1)

	var count int
	for i := N; i > 0; i-- {
		s := sumOfMultiple(output, N+1, i)
		if s%2 != input[i] {
			switch input[1]{
			case 0:
				output[i] = 1
				count++
			case 1:
				output[i] = 0
			}
		}
	}

	if input[1]%2 != output[1] {
		fmt.Print(-1)
	} else {
		fmt.Println(count)
		for i := 1; i <= N; i++ {
			if output[i] == 1{
				fmt.Print( i)
				if i != N{
					fmt.Print(" ")
				}
			}
		}
	}
	return
}

func sumOfMultiple(arr []int, size int, baseNum int) int {
	var sum int
	for i := baseNum; i < size; i += baseNum {
		sum += arr[i]
	}
	return sum
}

func maxInt(x, y int) int {
	if x > y {
		return x
	}
	return y
}
func scanNums(len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		fmt.Scan(&num)
		nums = append(nums, num)
	}
	return
}