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
	inputs = input.split("\n");

	var N = parseInt( inputs[0], 10 );

	var boxes = new Array( N );
	var inputArray = [];
	var inputCounter = 0;

	for ( var i = N; i > 0; i-- ) {
		var index = i - 1;
		var tmp = parseInt( inputs[i], 10 );

		var sum = 0;
		var counter = 2;
		while ( i * counter <= N) {
			sum += boxes[i * counter - 1];
			counter++;
		}

		if ( sum % 2 == tmp ) {
			boxes[index] = 0;
		} else {
			boxes[index] = 1;
			inputCounter++;
			inputArray.push(i);
		}
			
	}

	if ( inputCounter > 0 ){
		console.log('%d', inputCounter);

		for ( var i = inputCounter - 1; i >= 0; i-- ) {
			console.log( '%d', inputArray[i] )
		}
	} else {
		console.log('%d', 0);
	}

}
//*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"));