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: Runtime Error)

/**
 * @Author:      G_bg
 * @DateTime:    2019-07-20 20:22:09
 * @Description: 
 */
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const double PI = 3.1415926535898;
const double E = 2.718281828459;
const int INF = 0x7fffffff;
const int mod = 1e9+7;
const int maxn=2e5+10;
int a[maxn],b[maxn];
vector<int> v;
int main(int argc, char const *argv[]) {
	ios::sync_with_stdio(0);cin.tie(0);
	int n;cin >> n;
	for(int i = 1;i <= n;i++) cin >> a[i];
	for(int i = n/2+1;i <= n;i++){
		if(a[i] == 1) b[i] = 1,v.push_back(i);
	}
	bool flag = true;
	for(int i = n/2;i > 0;i--){
		int num = 0;
		for(int j = i;j <= n;j += i){
			if(b[i] == 1) num++;
		}
		if(num > a[i]) {
			flag = false;
			break;
		}else{
			if(a[i] == 1 && num == 0) b[i] = 1,v.push_back(i);
		}
	}
	if(!flag) cout << -1 << endl;
	else{
		cout << v.size() << endl;
		cout << v[0];
		for(int i = 1;i < v.size();i++)
			cout << " " << v[i];
		cout << endl;
	}
	//system("pause");
	return 0;
}