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.