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)

#include <bits/stdc++.h>
#include <iostream>
using namespace std;
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define modulo 1000000007
typedef long long int ll;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;

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

	vector<int> num(n+1);

	for(int m=2; m<=n; m++){
		int imin = (n%m==0)?(n/m):(n/m+1);
		int imax = (n%(m-1)==0)?(n/(m-1)):(n/(m-1)+1);
		for(int i=imin; i<imax; i++){
			int sum(0);
			for(int j=1; j<m; j++) sum += num[i*(j+1)];

			if(sum % 2 != a[i]) num[i] = 1;
			else num[i] = 0;
		}
	}

	int M(0);
	for(int i=1; i<n+1; i++) M += num[i];

	cout << M << endl;
	for(int i=1; i<n+1; i++){
		if(num[i]!=0) cout << num[i] << " ";
	}
	if(M!=0) cout << endl;

	return 0;
}