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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
int main(){
	int n; cin >> n;
	vector<int> a(n+1);
	for(int i=1;i<=n;i++) cin >> a[i];

	vector<int> b(n+1,0);
	int ones = 0;
	for(int i=n;i>=1;i--){
		int parity = 0;
		// int num = i+1;
		for(int j=i+i;j<=n;j+=i){
			if(b[j] == 1) parity = (1-parity);
		}
		// cout << "parity: "<< parity << " | expected: "<<a[i] << endl;
		if(parity != a[i]){
			b[i] = 1;
			ones++;
		}
	}
	// if(ones == 0){
	// 	cout << ones << endl;
	// 	return 0;
	// }

	cout << ones << endl;
	int i=1,j=0;
	while(i<=n && j<ones){
		if(b[i]==1){
			cout << i ;
			j++;
			i++;
			break;
		}
		i++;
	}
	for(;i<=n;i++){
		if(b[i] == 1){
			cout << " " << i; 
		}
	}
	if(ones > 0) cout << endl;
	return 0;
}