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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            a[i] = sc.nextInt();
        }

        // 後ろから順にボールが入っているかをXORで計算していく
        int[] ball = new int[n + 1];
        for (int i = n; i >= 1; i--) {
            int sum = 0;
            for (int j = i + i; j <= n; j += i) {
                // i倍数の部分だけ計算しなおす
                sum ^= ball[j];
            }
            // iとXORする
            ball[i] = sum ^ a[i];
        }

        int ballCount = (int) Arrays.stream(ball).filter(s -> s != 0).count();
        if (ballCount == 0) {
            System.out.println(0);
        } else {
            // 先にボールの個数を出力して、それ以外はボールが入っている場所だけ出力
            System.out.println(ballCount);
            for (int i = 1; i <= n; i++) {
                if (ball[i] == 0) {
                    continue;
                }
                System.out.println(i);
            }
        }
    }
}