Description

Given a positive integer $a$, decompose it into a product of several positive integers, i.e., $a= a_1× a_2× a_3 × ...×a_n$, where $1$<$a_1$≤$a_2$≤$a_3$≤ ...≤$a_n$. Find the number of different decomposition schemes. Note that $a = a$ is also considered a valid decomposition.

Input Format

The first line contains the number of test cases $n$ ($1≤n≤10$), followed by $n$ lines of input. Each test case consists of one line containing a positive integer $a$ ($1 < a < 32768$).

Output Format

$n$ lines, each containing the number of valid decomposition schemes for the corresponding input.

Sample

2
2
20

1
4