Given an integer $n > 1$, and the equation:

$$\frac{1}{n} = \frac{1}{a} + \frac{1}{b}$$

Find two distinct positive integers $a, b$ which both satisfy the above equation, and have a minimal sum $a + b$.

Input

• The only line of input consists of one integer $n$ ($1 < n \le 10^8$) — the number for the left hand side of the equation.

Output

Output the best choices for $a$ and $b$ in ascending order.

Examples

Input 1

4

Output 1

6 12

Input 2

107

Output 2

108 11556

Input 3

999999

Output 3

1998000 2002000

Input 4

1000000

Output 4

1800000 2250000