Divisible Repunit

Problem Description

Here the so-called "lonely number" does not refer to a single person~ it refers to a number consisting entirely of $1$s, such as $1, 111, 1111$, etc. Legend has it that any lonely number can be divided by an odd number that does not end with $5$. For example, $111111$ can be divided by $13$. Now your program should read an integer $x$, which is definitely an odd number and does not end with $5$. Then, after calculation, output two numbers: the first number $s$, meaning that $x$ multiplied by $s$ is a lonely number, and the second number $n$ is the number of digits of this lonely number. Such a solution is of course not unique; you are asked to output the smallest solution.

Hint: an obvious method is to gradually increase the number of digits of the lonely number until it is divisible by $x$. But the difficulty is that $s$ may be a very large number — for example, if the program inputs $31$, it should output $3584229390681$ and $15$, because $31$ multiplied by $3584229390681$ equals $111111111111111$, which has $15$ ones in total.

Input Format

A single line containing a positive odd number $x$ that does not end with $5$ ($x < 1000$).

Output Format

Output the corresponding smallest $s$ and $n$ in one line, separated by a single space.

Sample Input

31

Sample Output

3584229390681 15