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 JavaScript (node.js v5.12) (judge verdict: Accepted)



function Main(input) {
  input = input.split("\n");
  var N = parseInt(input[0]);
  var a = input[1].split(" ").map(i => parseInt(i));
  var bb = new Array(N).fill(0);
  var bsub = new Array();
  var num = 0;
  for(var i=N;i>0;i--){
    var cnt =0;
    for(var j=1;j*i<=N;j++){
      cnt+=bb[j*i-1];
    }
    if(cnt%2!=a[i-1]){
      num++;
      bsub.push(i);
      bb[i-1]++;
    }
  }
  var b = bsub.join(" ");
  var ans = num+"\n"+b;
  console.log('%s', ans);
  return ans;
}

function debug(n){
  var input = document.getElementById("input"+n).value;
  var ans=Main(input);
  var result="WA";
  if(ans==document.getElementById("output"+n).value.split("\n")[0]){
    result="AC";
  }
  document.getElementById("result"+n).innerHTML=result;
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));