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: Accepted)

#include<iostream>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<string>
#include<stdio.h>
#include<stdlib.h>
#include<float.h>
#include<tuple>
#include<string.h>
#include<iomanip>
#include<stack>
#include<queue>

using namespace std;
#define ll long long
#define rep(i,n) for(ll i=0;i<n;i++)
#define ALLOF(c) (c).begin(), (c).end()
#define Pa pair<ll,ll>
const ll mod=10e9+7;
const ll INF=10e12;
const ll inf=-1;
ll ABS(ll a){return max(a,-a);}

int main(void){
    ll N;
    cin>>N;
    vector<ll> A(N),B(N,0);
    rep(i,N) cin>>A.at(i);
    for(ll i=N;i>0;i--){
        ll kosu=0;
        for(ll j=2*i;j<=N;j+=i){
            kosu+=B.at(j-1);
        }
        if(kosu%2!=A.at(i-1)) B.at(i-1)=1;
    }
    vector<ll> ans(0);
    rep(i,N) if(B.at(i)) ans.push_back(i+1);
    cout<<ans.size()<<endl;
    if(ans.size()==0) return 0;
    rep(i,ans.size()-1) cout<<ans.at(i)<<" ";
    cout<<ans.at(ans.size()-1)<<endl;
    return 0;
}