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>
using namespace std;
#define ll long long
#define pll pair<ll,ll>
#define ff first
#define ss second
#define se set<ll>
#define vec vector<ll>
#define inf 10000000000000000
#define pri 100000000007
bool mark[100005];
vec adj[100005];
ll counter;
vec cnt;
vector<string> forsubs;

         
   



int main()
{    
 

   #ifdef APNA_IO
      freopen("input.txt","r",stdin);
      freopen("output.txt","w",stdout);
   #endif
          ios_base::sync_with_stdio(false); 
    cin.tie(NULL); 

  ll n;
  cin>>n;
  ll a[n+1];
  ll b=0;

  for(ll i=1;i<=n;i++)
  {
    cin>>a[i];
    if(i!=1)
    {
      if(a[i]==1)
        b++;
    }
  }

  if(b==0)
  { 
    if(a[1]==1)
    cout<<"1"<<"\n"<<"1"<<"\n";
    else
      cout<<"0"<<"\n";
  }
  else
    cout<<"-1"<<"\n";



}