Description

You are given an integer $n$, print $n$ integers $a_1,a_2,\cdots,a_n$ that satisfies $\displaystyle\sum_{i=1}^n a_i=\operatorname{lcm}(a_1,a_2,\cdots,a_n)$. You should also minimize $(\max_{i=1}^n a_i)-(\min_{i=1}^n a_i)$. $(1\le n\le 5\times 10^6)$.

Note that the least common multiple of the $n$ integers you print should not exceed $10^{12}$, or your answer will be judged as a wrong answer.

Input Format

The first line contains one integer $n$.

Output Format

Print your answer in any order seperated by space.

Do not print any spaces in the end of the line, or your answer will be judged as a wrong answer.

3

1 2 3

Hint

It can be proved that the range cannot be less that $2$ when $n=3$. Thus, this answer is acceptable. Besides, 1 3 2 , 3 2 1 are also acceptable answers.