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: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int N = Integer.parseInt(sc.next());
		int[] a = new int[N];
		int idx;
		for (idx = 0; idx < N; idx++) {
			a[idx] = Integer.parseInt(sc.next());
		}

		boolean ansFlg = true;

		int i;
		int ballSum = 0;
		int ballNum = 0;
		int[] ballIdx = new int[N];
		for (i = 1; i <= N; i++) {
			// iの倍数のボールの和
			ballSum = 0;
			for (idx = i; idx <= N; idx += i) {
				ballSum += a[idx - 1];
			}
			// ai の中身が i の倍数の総和 % 2かどうか
			if (a[i - 1] == (ballSum % 2)) {
				// 合ってるので、余り1だったらボール入れる
				if (a[i - 1] == 1) {
					ballIdx[ballNum] = i; // 1始まり
					++ballNum;
				}
			} else {
				// 解なし
				ansFlg = false;
				break;
			}

		}

		if (ansFlg) {
			System.out.println(ballNum);
			if (ballNum > 0) {
				for (idx = 0; idx < ballNum; idx++) {
					if (idx > 0) {
						System.out.print(" ");
					}
					System.out.print(ballIdx[idx]);
				}
				System.out.println();
			}
		} else {
			System.out.println(-1);
		}

	}

}