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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input) {
	input = input.split("\n");
	const N = parseInt(input[0])
	const As = input[1].split(" ").map(x => parseInt(x))
	const boxs = new Array(N)
	boxs.fill(1)
	for(i=0; i < N; i++){
		var id = N-i
		var sum = 0
		for(j=1; j <= N/id; j++){
			sum = (sum + boxs[j*id-1]) % 2
		}
		if(sum != As[id-1]) boxs[id-1] = 0
	}
	var results = ""
	var count = 0
	for(i=0; i < N; i++){
		if(boxs[i] == 1){
			count++
			results += " " + (i+1)
		}
	}
	console.log(count)
	if(results != "") console.log(results.slice(1))
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));