Counting Distinct Rectangular Pairs

Given a positive integer n, your task is to determine the number of distinct ordered pairs of positive integers (a, b) such that $a \times b = n$.

Note that the pair (a, b) is considered different from (b, a) if a \neq b. For example, if n = 6, the valid pairs are (1, 6), (2, 3), (3, 2) and (6, 1), thus the answer is 4.

You are required to handle multiple test cases.

inputFormat

The first line of input contains an integer T representing the number of test cases. Each of the following T lines contains a single integer n (1 \leq n \leq 10^{12}).

outputFormat

For each test case, output a single line containing the number of distinct ordered pairs (a, b) such that $a \times b = n$.

## sample

5
6
12
1
16
1000000000

4
6
1
5
100

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