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 <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<ll> vl;
typedef long double ld;
typedef vector<ld> vd;
typedef bool bl;
typedef vector<bl> vb;
typedef vector<vl> mt;
typedef unordered_map<ll,unordered_map<ll,ll>> graph;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<string> vs;
typedef vector<vs> table;


const ll e5 = 1 << 20;
const ll mod = 1000000007;
const ll e3 = 1 << 13;
const ll INF = 1ll << 50;

ll n;
vl a;
vl b;

int main(){
  cin >> n;
  a = vl(n+1);
  b = vl(n+1);
  for(ll i = 1;i <= n;i++) cin >> a.at(i);
  for(ll i = n;i >= 1;i--){
    ll cnt = 0;
    for(ll j = 1;j*i <= n;j++){
      cnt += b.at(j);
    }
    if(cnt%2 == a.at(i)) continue;
    else b.at(i) = 1;
  }
  cout << accumulate(b.begin(),b.end(),0ll) << endl;
  for(ll i = 1;i <= n;i++){
    if(b[i] == 1) cout << i << " ";
  }
  cout << endl;

}