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)

#define _USE_MATH_DEFINES
#include <iostream>
#include <string>
#include <queue>
#include <vector>
#include <algorithm>
#include <math.h>
#include <map>
#include <list>
#include <iomanip>
#include <queue>
#include <cmath>
#include <numeric>
#define repl(i, l, r) for (ll i = l; i < r; i++)
#define rep(i, n) repl(i, 0, n)

using namespace std;
using ll = long long;
typedef pair<ll, ll> p;
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
const long long mod = 1e9 + 7;
ll gcd(ll a, ll b);
ll lcm(ll a, ll b);

vector<int> to[200005];
vector<int> ans;
ll gcd(ll a, ll b);

int main() {
	int n;
	cin >> n;

	vector<int> a(n + 1);
	rep(i, n) cin >> a[i + 1];
	
	vector<int> b(n + 1);
	
	ll sum = 0;

	for (int i = n; i > 0; i--) {
		ll j = n / i, tot = 0;
		while (j != 1) {
			tot += b[j * i];
			j--;
		}
		if (tot % 2 != a[i]) {
			b[i] = 1;
			sum++;
		}
	}

	if (sum == 0) cout << 0;
	else {
		cout << sum << endl;
		repl(i, 1, n + 1) {
			if (b[i] == 1) cout << 1 << " ";
		}
	}
	return 0;
}


ll gcd(ll a, ll b) {
	if (a % b == 0)return(b);
	else return(gcd(b, a % b));
}
ll lcm(ll a, ll b) {
	return a * b / gcd(a, b);
}