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 1 [5%]
Subtask 2 [45%]
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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