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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)


import java.util.Scanner;

public class Main {
	static int intN =0;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String n = sc.nextLine();
        String[] a1 = sc.nextLine().split(" ");

        intN = Integer.parseInt(n);

        String result2="";
        int cnt=0; // 2行目に何個1があるか
        for (int i = 0;i < intN; i++) {
        	if ("1".equals(a1[i])) {
        		cnt++;
        	}
        }
        int result1=cnt;
        if (cnt==0) {
        	System.out.println("0");
        } else if (cnt%2==0) {
          System.out.println("-1");
        } else {
        	for (int i = 0;i < intN; i++) {
        		if (i > 1 && warikiri(i)) {
        			continue;
        		}
        		String temp="";
        		if (cnt!=0) {
        			temp=String.valueOf(i+1);
        			cnt--;
        		}

        		if (!"".equals(temp)) {
        			if ("".equals(result2)) {
            			result2=temp;
        			} else {
        				result2=" " + temp;
        			}
        		}

            }
        	System.out.println(result1);
        	System.out.println(result2);
        }

    }

    // 自分以外で割り切れたらtrue
    // 自分以外で割り切れなかったらfalse
    private static boolean warikiri(int param) {
    	for (int i = 2;i < intN;i++) {
    		if (param%i==0 && i!=param) {
    			return true;
    		}
    	}

    	return false;
    }
}