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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

# include <bits/stdc++.h>
# define speed ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
# pragma GCC target("avx2")
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
# define int long long
  
using namespace std;
  
const int N = 1e3 + 7;
const int mod = 1e9 + 7;

int32_t main() {
    speed;
    int n;
    cin >> n;
    vector < int > a(n), ans(n);
    for ( auto &i: a ) {
        cin >> i;
    }
    vector < int > vc; 
    for ( int i = n / 2 + 1; i < n; i++ ) {
        ans[i] = a[i];
        if ( a[i] ) {
            vc.push_back( i + 1 );
        }
    }
    for ( int i = n / 2; i >= 0; i-- ) {
        int x = i + 1, sum = 0;
        while ( x <= n ) {
            sum += ans[x - 1];
            x += i + 1;
        }
        if ( x & 1 ) {
            if ( !a[i] ) {
                ans[i] = 1;
                vc.push_back( i + 1 );
            } 
        }
        else {
            if ( a[i] ) {
                ans[i] = 1;
                vc.push_back( i + 1 );
            }
        }
    }
    cout << vc.size() << '\n';
    for ( auto i: vc ) {
        cout << i << ' ';
    }
}