## HHPC1 P4 - Yet Another A+B Problem

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 256M

Author:
Problem type

Ryan is completing his math assignment where he stumbles upon a curious problem: find the number of pairs of positive integers that satisfy the equation . The assignment is too easy for him, so he generalises the problem: find the number of ordered pairs of positive integers which satisfy for a given positive integer .

Can you help Ryan solve this redesigned math problem?

#### Constraints

For all subtasks:

##### Subtask 3 [50%]

No additional constraints.

#### Input Specification

The first line contains a single integer , the number of test cases.

The following lines each contain a single integer .

#### Output Specification

For each test case, print a single integer, the number of ordered positive integer pairs that satisfy . It can be proven that the answer can fit in a 64-bit signed integer.

#### Sample Input

2
1
3

#### Sample Output

1
3

#### Sample Explanation

For the first test case, only satisfies the condition.

For the second test case, , and satisfy the condition.

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