Problem Description

Given a positive integer $ N $.

Construct one set of integers $(a,b,c,d,e,f)\ (1 \le a,b,c,d,e,f \le N)$ that satisfies $\dfrac{a}{b} < \dfrac{c}{d} < \dfrac{e}{f}$ and minimizes $\dfrac{e}{f} - \dfrac{a}{b}$.

Under the constraints of this problem, there always exists a set of integers $ (a,b,c,d,e,f) $ that satisfies $\dfrac{a}{b} < \dfrac{c}{d} < \dfrac{e}{f}$.

Input Format

The input is given from the standard input in the following format:

$ N $

Output Format

Output the answer $ (a,b,c,d,e,f) $ in this order, separated by spaces. If multiple solutions exist, any of them will be considered correct.

Sample Input and Output

Sample Input #1

2

Sample Output #1

1 2 1 1 2 1

Sample Input #2

3

Sample Output #2

1 3 1 2 2 3

Notes/Hints

Constraints

• $2 \le N \le 10^9$
• All inputs are integers

Sample Explanation 1

$\dfrac{1}{2} < \dfrac{1}{1} < \dfrac{2}{1}$. Answering with 1 2 2 2 2 1 would also be correct.

Sample Explanation 2

Original idea: [MATH0]

见题面 Input 部分

见题面 Output 部分