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 rep(i, n) for (int i = 0; i < (int)(n); i++)
using ll=long long;
const int MOD=(int)1e9+7;
const int INF=(int)1e9;
const ll LINF=(ll)1e18;

int main(){
    int n;cin >> n;
    vector<bool> a(n+1);
    rep(i,n){
        int t;cin >> t;
        if(t) a[i+1] = true;
        else a[i+1] = false;
    }
    vector<bool> ans(n+1,false);
    for(int i=n;i>=1;i--){
        bool yes = false;
        for(int j=i;j<=n;j += i){
            if(ans[j]) yes = !yes;
        }
        if(a[i] + yes == 1){
            ans[i] = true;
        }
    }
    int m=0;
    rep(i,n+1){
        m += ans[i];
    }
    cout << m << endl;
    bool ok=false;
    rep(i,n){
        if(ans[i]){
            cout << i << " ";
            ok = true;
        }
    }
    if(!ok) cout << 0;
    cout << endl;
}