Preparing Boxes

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.

Examples

Input

3 1 0 0

Output

1 1

Input

5 0 0 0 0 0

Output

0

inputFormat

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

outputFormat

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.

Examples

Input

3 1 0 0

Output

1 1

Input

5 0 0 0 0 0

Output

0

样例

5
0 0 0 0 0

0