Minimum Divisible Sequence

Обмеження: 2 сек., 512 МіБ

You are given an integer $n$.

Construct an integer sequence $a$ of length $m$ satisfying the following conditions.

• $1 \le a_i \le n$ for all $1 \le i \le m$.

• For each $1 \le k \le n$, there exists $1 \le i \le m$ such that $a_i$ is a multiple of $k$.

• The length $m$ is minimum possible.

Вхідні дані

The single line contains an integer $n$.

Вихідні дані

In the first line print an integer $m$ – the length of the sequence $a$.

In the second line print $m$ integers $a_i$ – the elements of the sequence.

If there are multiple answers, any of them will be accepted.

Обмеження

$1 \le n \le 10^5$.

Приклади

Вхідні дані (stdin) копіювати	Вихідні дані (stdout) копіювати
7	4 4 7 5 6

Примітки

In the example, one of the possible sequences is $a = (4, 7, 5, 6)$.

• $a_1 = 4$ is a multiple of $1$.

• $a_1 = 4$ is a multiple of $2$.

• $a_4 = 6$ is a multiple of $3$.

• $a_1 = 4$ is a multiple of $4$.

• $a_3 = 5$ is a multiple of $5$.

• $a_4 = 6$ is a multiple of $6$.

• $a_2 = 7$ is a multiple of $7$.

It is impossible to construct a sequence satisfying the conditions of length less than four.