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 <bits/stdc++.h>

#define rep(i, N) for (ll i = 0; i < N; i++)
#define rep1(i, N) for (ll i = 1; i <= N; i++)
#define repr(i, N) for (ll i = N-1; i >= 0; i--)

using ll = long long;
using namespace std;

typedef pair<int,int> P;
typedef vector<int> vi;

int main() {
    int N, M = 0;
    cin >> N;
    vi a(N), b(N);
    rep(i, N) cin >> a[i];
    repr(i, N) {
        ll asum = 0;
        rep1(j, N/(i+1) - 1) {
            asum += b[i + j*(i+1)];
        }
        asum %= 2;
        b[i] = (a[i] - asum + 2)%2;
        if(b[i] == 1) M++;
    }

    cout << M << "\n";
    rep(i, N) {
        if(b[i] == 1) cout << (i+1) << " ";
    }
    
    return 0;
}