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;
#define ll long long int
#define MOD 1000000007
#define ff first
#define ss second
#define pb push_back
#define N 505

#define mod 998244353

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	
	int n;
	cin >> n;
	int a[n + 1], max = 0, pos = 0, k = 0;
	for (int i = 1; i <= n; ++i)
	{
		cin >> a[i];
	}

	int f = 1;
	int m = 0;
	int b[n + 1];
	memset(b, -1, sizeof(b));

	for(int i = 1; i <= n; ++i)
	{
		b[i] = a[i];
	}

	for(int i = 1; i <= n; ++i)
	{
		int k = 0;
		for(int j = i; j <= n; j += i)
		{
			if(b[j]) k++;
		}
		if(a[i] != k % 2)
		{
			f = 0;
			break;
		}
	}

	if(f)
	{
		for (int i = 0; i < n; ++i)
		{
			if(b[i + 1]) m++;
		}
		cout << m << "\n";
		for (int i = 0; i < n; ++i)
		{
			if(b[i+1]) cout << i + 1 << " ";
		}
	}
	else
		cout << -1;
	return 0;
}