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 <set>
#include <map>
#include <list>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <cstdio>
#include <vector>
#include <string>
#include <bitset>
#include <cctype>
#include <cstdlib>
#include <cstring>
#include <utility>
#include <numeric>
#include <complex>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <cassert>
#include <iostream>
#include <iterator>
#include <algorithm>
using namespace std;
typedef long long ll;
const double EPS = 1e-9;
typedef vector<int> vint;
typedef pair<int, int> pint;
#define inf 1e+9
#define rep(i, n) REP(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define MSG(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
template<class T, class C> void chmax(T& a, C b){ a>b?:a=b; }
template<class T, class C> void chmin(T& a, C b){ a<b?:a=b; }

int main (){
	cin.tie(0);
   	ios::sync_with_stdio(false);

    int n,k,ans=0;
	cin >> n;
	vint v(n);
	vint t(n);
	rep(i,n){
		cin >> v[i];
		t[i] = 0;
	}

	int m=n,count=0;

	while(m!=0){
		for(int i=m-1;i>=m/2;i--){
			int j=2*i;
			int sum=0;
			if(m==1){
				for(j=1;j<n;j++){
					sum += t[i];
				}
			}
			else{
			while(j<n){
				sum += t[j];
				j += i;
			}
			}
			if(v[i]==0){
				t[i] = sum%2;
			}
			else{
				t[i] = (sum%2+1)%2;
			}
			if(t[i]==1){
				count++;
			} 
		}
		m=m/2;
	}

	cout << count << endl;

	rep(i,n){
		if(t[i]==1){
			cout << i+1 << " ";
		}
	}
	cout << endl;
}