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: Wrong Answer)

// inputに入力データ全体が入る
function Main(input) {
    // 1行目がinput[0], 2行目がinput[1], …に入る
    input = input.split("\n");
    tmp0 = input[0].split(" ");
    tmp1 = input[1].split(" ");
    N = Number(tmp0[0])
    a = []
    x = []
    for(var i=0; i<N; i++)
    {
        a.push(Number(tmp1[i]))
        x.push(0)
    }

    // i
    for(var i=N; i>0; i--)
    {
        a[i-1]
        // aiを計算
        var tmp_ai=0
        for(var j=1; j<=N;j++)
        {
            if(j%i === 0 && x[j-1] === 1)
            {
                tmp_ai+=1
            }
        }
        if(a[i-1] === (tmp_ai % 2)){
            continue
        }else{
            x[i-1] = 1
        }
    }
    // console.log(x)
    console.log(x.filter(a => a===1).length)
    for(var i=0; i<N; i++)
    {
        if(x[i] === 1){
            process.stdout.write(i + " ")
        }
    }
}
  //*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));
// Main("6\n0 1 0 1 0 1\n");