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 <iostream>
#include <iomanip>
#include <map>
#include <set>
#include <vector>
#include <utility>
#include <algorithm>
#include <queue>
#include <cstdint>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

constexpr ll inf = INT64_MAX / 4;
constexpr ll mod = 1000000007;

constexpr int maxn = 200000;

int n, a[maxn + 1], c[maxn + 1], r[maxn + 1];

set<int> prime;

map<int, int> fac_p(int m) {
    int k = m;
    map<int, int> s;
    for (auto e:prime) {
        while (k % e == 0) {
            k = k / e;
            s[e]++;
        }
    }
    if(k != 1) s[k]++;
    return s;
}

set<int> divisor(int m) {
    auto t = fac_p(m);
    set<int> s[2];
    s[1].insert(1);
    int i = 0;
    for (auto e:t) {
        for (auto f:s[(i+1) % 2]) {
            for (int j = 0; j <= e.second; j++) {
                s[i % 2].insert(f * pow(e.first, j));
            }
        }
        s[(i+1) % 2].clear();
        i++;

    }
    return s[(i+1) % 2];
}

int main() {
    for (int i = 2; i * i <= maxn; i++) {
        bool flag = true;
        for (auto e:prime) {
            if (i % e == 0) {
                flag = false;
                break;
            }
        }
        if (flag) prime.insert(i);
    }
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
    }
    for (int i = n; i > 0; i--) {
        if (c[i] != a[i]) {
            r[i] = 1;
            for(auto e:divisor(i)) {
                c[i] = (c[i]+1)%2;
            }
        }
    }
    set<int> v;
    for(int i = 1;i <= n;i++) if(r[i]) v.insert(i);
    cout << v.size() << endl;
    for(auto e:v) cout << e << " ";
    cout << endl;
}