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 <cstdio>
#include <cassert>
#include <algorithm>    
#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <iomanip>
#include <cstring>
#include <cmath>
#include <bitset>
#define pb push_back
#define mk make_pair
#define eb emplace_back
#define eps 1e-8
#define fi first
#define se second
#define all(x) (x).begin(),(x).end()
#define int long long
using namespace std;

typedef long double ld;
typedef unsigned int ui;
typedef pair<int,int> pii;
typedef tuple<int, int, int> tiii;
typedef unsigned long long ull; 
typedef vector<int> vii;
typedef vector<long double> vd;
const int inf = 1e9;
const int INF = 1e18;
const int M = 1e9 + 7;
//__int128
const int maxn = 3e5;
int a[maxn], b[maxn];
signed main()
{
#ifndef ONLINE_JUDGE
    //freopen("in.txt", "r", stdin);
    // freopen("out.txt", "w", stdout);
#endif
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, res = 0;
    cin >> n;
    for(int i = 1; i <= n; ++i) {
    	cin >> a[i];
    	if(a[i] & 1) {
    		++res;
    	}
    }
    cout << res << endl;
    for(int i = 1; i <= n; ++i) {
    	if(a[i] & 1) {
    		cout << i << endl;
    	}
    }
    return 0;
}