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.

## Comments