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: Time Limit Exceeded)

// Package main provides
//
// File:  main.go
// Author: ymiyamoto
//
// Created on Sat Jul 20 21:17:55 2019
//
package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)
	arr := make([]int, n)
	for i := range arr {
		fmt.Scan(&arr[i])
	}
	arr = append([]int{0}, arr...)

	bs := make([]int, len(arr))
	for i := n; i > 0; i-- {
		num := 0
		for j := i + 1; j <= n; j++ {
			if j%i == 0 {
				num += bs[j]
			}
		}
		if arr[i] != num%2 {
			bs[i] = 1
		}
	}
	ans := make([]int, 0)
	for i := 1; i <= n; i++ {
		if bs[i] == 1 {
			ans = append(ans, i)
		}
	}

	fmt.Println(len(ans))
	for i := range ans {
		if i != 0 {
			fmt.Print(" ")
		}
		fmt.Print(ans[i])
	}
	fmt.Println()
}