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.*;
import java.io.*;
import java.util.stream.Stream;

public class Main {
    public static void main(String[] args) throws Exception {
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(br.readLine());
        String[] strA = br.readLine().split(" ");
        int[] A = Stream.of(strA).mapToInt(Integer::parseInt).toArray();
        
        // ボールを入れるか入れないか
        int[] B = new int[N];
        List<Integer> list = new ArrayList<>();
        
        for(int i = N; i >= 1; i--){
            
            int boxNum = i;
            int baisuu = 1;
            int ballCount = 0;
            while( boxNum <= N ) {
                ballCount += B[boxNum-1];
                boxNum *= ++baisuu;
            }

            if ( A[i-1] == 0 && ballCount % 2 == 0 ) continue;
            if ( A[i-1] == 1 && ballCount % 2 == 1 ) continue;
            B[i-1] = 1;
            list.add(i);
        }
        
        System.out.println(list.size());
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < list.size(); i++){
            sb.append(list.get(i));
            if (i != list.size() -1) sb.append(" ");
        }
        
        System.out.println(sb);
    }
}