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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 2e6 + 5;
bool mark[N];
int a[N];
vector <int> q;
int main()
{
	ios::sync_with_stdio(false);
	int n;
	cin >> n;
	q.clear();
	memset(mark, 0, sizeof(mark));
	for(int i = 1; i <= n; i ++)
	{
		int d;
		cin >> d;
		a[i] = d;
		if(d == 0)
			for(int j = i; j <= n; j += i)
				mark[j] = true;
		else 
			q.push_back(i);
	}
	if(q.size() == 0)
	{
		cout << 0 << endl;
		return 0;
	}
	if(q.size() == 1)
	{
		if(a[1])
		{
			cout << 1 << endl;
			cout << 1 << endl;
		}
		else 
			cout << -1 << endl;
		return 0;
	}
	int dd = q[1], zz = q[1];
	for(int i = 2; i < q.size(); i ++)
	{
		dd = __gcd(dd, q[i]);
		zz = 1ll * zz * q[i] / __gcd(zz, q[i]);
	}
	cout << zz << endl;
	if(a[1] == 0 && q.size() >= 0 || a[1] == 1 && (dd == 1 || zz > n || mark[zz] == true))
	{
		cout << -1 << endl;
		return 0;
	}
	cout << 1 << endl;
	cout << zz << endl;

}