Number of pairs

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Integer Factorization, Algorithms, Math, Mathamatics, Factorization, Number Theory

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Problem

You are given an integer which is a product of LCM and GCD. Your task is to find all the pairs of $x$ and $y$ for which their product of LCM and GCD is equal to the given number.

Note: Pair $x$ and $y$ is different from $y$ and $x$ .

Input format

The first line of the input contains a single integer $T$ denoting the number of test cases.
The first and only line of each test case contains a single Integer.

Output format

For each test case, print a single line containing the Integer.

Constraints

$1 \le T \le 100$
$1 \le N \le 4 \times 10^9$

Time Limit: 1

Memory Limit: 256

Source Limit:

Explanation

For test input 1, N= 1, only pair is (1, 1).

For test input 2, N = 2, pair will be (1, 2) and (2, 1).

For test input 3, N = 16, pair will be (1, 16), (2, 8), (4, 4), (8, 2), (16, 1).