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 ll long long
#define pq priority_queue
using namespace std;
const ll INF=(ll)1e9;
const ll MOD=(ll)1e9+7;
const ll MAX=510000;
vector<int> dx={1,0,-1,0},dy={0,1,0,-1};
template<class T> inline bool chmax(T& a, T b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a>b) { a=b; return 1; } return 0; }

int main(){
    ll N,M=0,cnt=0;
    cin>>N;
    ll a[N];
    vector<ll> ans(N,0),kotae(N,0);
    for(ll i=0;i<N;i++) cin>>a[i];
    for(ll i=N-1;i>=0;i--){
        if(ans[i]%2!=a[i]) kotae[i]++;
        for(ll j=1;j<=i+1;j++){
            if((i+1)%j==0) ans[(i+1)/j]+=a[i];
        }
    }
    for(ll i=0;i<N;i++){
        if(kotae[i]) M++;
    }
    cout<<M<<endl;
    for(ll i=0;i<N;i++){
        if(cnt!=M-1&&kotae[i]){
            cout<<i+1<<" ";
            cnt++;
        }else if(cnt==M-1&&kotae[i]){
            cout<<i+1<<endl;
        }
    }
}