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>

#define debug(n) cerr << #n << ':' << n << endl;

using namespace std;

using  ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using  vi = vector<int>;
using  vl = vector<ll>;
using  vd = vector<double>;
template<class T,class U>
using umap = unordered_map<T,U>;
template<class T>
using uset = unordered_set<T>;

template<class T>
inline bool change_max(T&a, const T&b){
  if(b > a){
    a = b;
    return true;
  }
  return false;
}

template<class T>
inline bool change_min(T&a, const T&b){
  if(a > b){
    a = b;
    return true;
  }
  return false;
}

template<class T>
inline void putv(const vector<T>&v,char c = '\n'){
  for(auto&&e:v){
    cout << e << c;
  }
}

void add_map(map<int,int>&mp,int n){
  for(int i = 1; i*i<=n; ++i){
    if(n % i == 0){
      mp[i]++;
      if(i!=n/i)mp[n/i]++;
    }
  }
}

int main(){
  int n; cin >> n;
  vi v(n);
  for(auto&&e:v){
    cin >> e;
  }
  vi ans;
  map<int , int>mp;
  int cnt = 0;
  for(int i = n - 1; i >= 0; --i){
    int c = mp.count(i+1);
    if(v[i] != c%2){
      ans.push_back(i+1);
      add_map(mp,i+1);
    }
  }
  cout << ans.size() << endl;
  putv(ans,'\n');
  return 0;
}