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)

"use strict";

const input = require("fs").readFileSync("/dev/stdin", "utf8");

const inputs = input.split("\n");
const N = Number(inputs[0]);
const arr = inputs[1]
  .trim()
  .split(" ")
  .map(Number);

const main = (N, arr) => {
  let answer = [];
  let ballNum = 0;

  let ai;
  let box = new Array(N).fill(0);
  for (let i = arr.length - 1; i >= 0; i--) {
    // 大きい箱から順番に取り出す
    ai = arr[i];

    let sum = 0,
      j = i + 1;
    while (j + i + 1 <= N) {
      // iを加算していき、Nを超えるまで中のaiを加算し続ける。
      sum += box[j + i];
      j += i + 1;
    }
    // 結果をもとに、箱にたまを入れるかを決定する
    if (sum % 2 == ai) {
      // ボールを入れない
    } else if ((sum + 1) % 2 == ai) {
      // ボールを入れる
      ballNum++;
      answer.push(i + 1);
      box[i]++;
    } else {
      return -1;
    }
  }
  answer = answer.reverse();
  // 回答用の配列に格納
  if (ballNum == 0) {
    return 0;
  } else {
    return `${ballNum}
${answer.join(" ")}`;
  }
};
console.log(main(N, arr));