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 <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <cstring>
#include <queue>
#include <stack>
#include <cmath>
#include <iterator>
#include <vector>
#include <string>
#include <set>
#include <iostream>
#include <random>
#include <map>
#include <iomanip>
#include <stdlib.h>
#include <list>
#include <typeinfo>
#include <list>
#include <set>
#include <cassert>
#include <fstream>
#include <unordered_map>
#include <cstdlib>
#include <complex>
#include <cctype>
#include <bitset>
using namespace std;

using ll = long long;
using vll = vector<long long>;
using pll = pair<long long, long long>;
#define rep(i,n) for(long long i(0);(i)<(n);(i)++)

const long long MOD = 2;

void solve(long long N, std::vector<long long> a){
    vector<bool> ans(N+1, false);
    for(ll i= N; i>0; i--){
        ans[i] = (bool) a[i-1];
        for(ll k=2*i; k<= N; k+= i){
            if(ans[k]) 
                ans[i] = !ans[i];
        }
    }
    ll sum = 0;
    for(ll i=1; i<= N; i++){
        if(ans[i])
            sum++;
    }
    cout << sum << endl;
    vll res;
    if(sum > 0){
        for(ll i=1; i<= N; i++){
            if(ans[i])
                res.push_back(i);
        }
    }
    rep(i, res.size()){
        if(i != res.size()-1)
            cout << res[i] << ' ';
        else
            cout << res[i] << endl;
    }
}

int main(){
    long long N;
    scanf("%lld",&N);
    std::vector<long long> a(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&a[i]);
    }
    solve(N, std::move(a));
    return 0;
}