The Game Is Back On

Moriarty is bored again. When he gets bored, the only thing he wants to do is play with Sherlock. So he has given Sherlock another one of his puzzles. Will you help him solve it?

Moriarty has given Sherlock a number N. Now, Sherlock has to determine how many pairs of numbers (A, B) exists such that A and B are coprime with each other and LCM of A and B is N. Here, LCM means Least Common Multiple. Please note that two pairs (A, B) and (B, A) are considered the same and will be counted only once for the final answer.

Two numbers are coprime with each other if there is no number other than 1 that divides both of these numbers.

Input

In the first line of the input, there will be a number T (1 ≤ T ≤ 300) denoting the number of test cases. In the next T lines there will be a number N (1 ≤ N ≤ 1012) as described above.

Output

For each case, print the answer to Moriarty's puzzle in a single line.

Sample

Input	Output
2 3 42	1 4