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: Time Limit Exceeded)

'use strict'

const divisors = n => {
  let dest = []
  for (let i = 1; i < Math.floor(Math.pow(n, 0.5) + 1); i++) {
    if (n % i === 0) {
      dest.push(i)
      if (Math.floor(n / i) !== i) {
        dest.push(Math.floor(n / i))
      }
    }
  }
  return dest.sort((a, b) => a - b)
}

function main(inp) {
  inp = inp.trim().split('\n')
  const N = Number(inp.shift())
  inp = inp[0].split(' ').map(n => Number(n));
  inp.unshift(0)

  let ans = []
  let allBalls = new Array(N+1).fill(0)

  for (let i = N; i > 0; i--) {
    if (inp[i] > 1) return console.log(-1)
    if (allBalls[i] % 2 !== inp[i]) {
      ans.unshift(i)
      
      let arr = divisors(i)
      for (let j = 0; j < arr.length; j++) {
        allBalls[arr[j]]++
      }
    }
  }
  if (ans.length) {
    console.log(ans.length)
    console.log(ans.join(' '))
  } else {
    console.log(0)
  }
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));