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 <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <cstring>
#include <map>
#include <set>
#include <queue>
#include <math.h>
#include <unordered_map>
#include <algorithm>

#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define all(x) (x).begin(),(x).end()
inline int gcd(int a,int b){return b?gcd(b,a%b):a;}
inline int lcm(int a,int b){return a*b/gcd(a,b);}
typedef long long ll;
typedef std::vector<int> VI;
typedef std::pair<int, int> PII;

using namespace std;

int main()
{
  int N;
  cin >> N;
  vector<int> A(N+1);
  vector<int> B(N+1, 0);
  int count = 0;
  REP(i,N+1) cin >> A[i+1];
  for (int i=N-1;i>0;i--)
  {
    int t = 0;
    for (int j=i*2;j<N;j+=i)
    {
      if (B[j]) t = 1-t;
    }
    if (A[i] != t)
    {
      B[i] = 1;
      count++;
    }
  }
  int count2 = 0;
  printf("%d\n", count);
  for (int i = 1; i < N+1; i++)
  {
    if (B[i])
    {
      count2++;
      if (count2 == count)
      {
        printf("%d\n", i);
      } else {
        printf("%d ", i);
      }
    }
  }
  return 0;
}