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) {
    var N = parseInt(input[0], 10);
    var A = input.slice(1).map(a => parseInt(a, 10));

    var goodArray = new Array(N);
    var sum = 0;
    var times = 2;
    var index = 0;

    for (var i = N; i > 0; i--) {
        sum = 0;
        times = 2;
        index = times * i;
        while(index <= N) {
            sum += goodArray[index - 1];
            times++;
            index = times * i;
        }
        if ((A[i - 1]) % 2 === 0) {
            goodArray[i - 1] = sum % 2 === 0 ? 0 : 1;
        } else {
            goodArray[i - 1] = sum % 2 === 0 ? 1 : 0;
        }
    }

    var result = 0;
    for (var j = 0; j < N; j++) {
        result += goodArray[j];
    }

    if (result === 0) {
        return console.log(0);
    } else {
        console.log(result);
    }

    var resultArray = goodArray.map((num, index) => {
        return num === 1 ? index + 1 : 0;
    })

    console.log(resultArray.filter(num => num !== 0).join(' '));
  }

  Main(require("fs").readFileSync("/dev/stdin", "utf8").trim().split(/\n|\s/));