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 <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <algorithm>
#include <numeric>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <climits>
#include <cmath>
#include <cstring>
#include <unordered_set>
#include <unordered_map>
using namespace std;

#define pb push_back
#define fst first
#define snd second

typedef long long ll;
typedef pair<int,int> pii;
template<typename T> using min_queue=priority_queue<T,vector<T>,greater<T>>;

const ll MOD=1e9+7;

int N;
int a[200100];
int b[200100];

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

  cin>>N;
  for(int i=1;i<=N;i++) cin>>a[i];
  vector<int> res;
  for(int i=N;i>=1;i--){
    int s=0;
    for(int j=N/i*i;j>i;j-=i) s+=b[i];
    b[i] = (s&1)^a[i];
    if (b[i]) res.pb(i);
  }
  cout<<res.size()<<endl;
  for(int k:res) cout<<k<<" ";
  cout<<endl;

  return 0;
}