LCM Cardinality#1247
A pair of numbers always has a unique LCM, but a single number can be the LCM of several different pairs of numbers. For example, is the LCM for the pairs , , , and so on. For a given positive integer , the number of different integer pairs whose LCM is is called the LCM cardinality of . Given a number, you need to find the value of its LCM cardinality.
The input consists of at most lines. Each line is a separate test case and contains an integer (0 < N \leq 2 \cdot 10^9). The last line contains a single zero and should not be processed.
For each test case, output two integers and on a separate line. Here, is the input number, and is its LCM cardinality. The printed numbers should be separated by a single space.
Example 1