Description

Given a positive integer ( a ), it is required to decompose it into a product of several positive integers, i.e., ( a = a_1 \times a_2 \times a_3 \times \dots \times a_n ), where ( 1 < a_1 \leq a_2 \leq a_3 \leq \dots \leq a_n ). The number of such decomposition methods is to be determined. Note that ( a = a ) itself is also considered a valid decomposition.

Input Format

The first line contains the number of test cases ( n ), followed by ( n ) lines of input. Each test case consists of a single line with a positive integer ( a ) (( 1 < a < 32768 )).

Output Format

Output ( n ) lines, each corresponding to an input. Each line should contain a positive integer indicating the number of valid decomposition methods for the given input.

## Sample Input
2
2
20

## Sample Output
1
4

Explanation of the Sample Output:

• For ( a = 2 ), the only decomposition is ( 2 ) itself.
• For ( a = 20 ), the valid decompositions are:
  1. ( 20 )
  2. ( 2 \times 10 )
  3. ( 4 \times 5 )
  4. ( 2 \times 2 \times 5 )

```input1
2
2
20

1
4