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>
using namespace std;

#define REP(i, start, count) for(int i=(start); i<(int)(count); ++i)
#define rep(i, count) REP(i, 0, count)
#define ALLOF(c) (c).begin(), (c).end()

typedef long long ll;
typedef unsigned long long ull;

int main(void) {
    int N;
    cin >> N;
    vector<int> a(N + 1);

    REP(i, 1, N + 1) cin >> a[i];

    vector<int> ans(N + 1);
    int M = 0;
    for (int i = N; i >= 1; --i) {
        int k = i + i;
        int odd = 0;
        while (k <= N) {
            odd = (odd + ans[k]) % 2;
            k += i;
        }

        if (a[i] != odd) {
            ans[i] = 1;
            M++;
        }
    }

    cout << M << endl;
    rep(i, N + 1) {
        if (ans[i] == 1) {
            cout << i;
            if (i != N) cout << " ";
        }
    }
    cout << endl;

    return 0;
}