Alice is very good in mathematics. So, his teacher gave him a number N and wants from him to count total number of pairs, such that $gcd( x ,y )=1$ and $x*y=N$, where $(x, y)$ forms a pair.

Alice is very busy in his exams and he wants your help .So solve this problem for Alice.

Input:
Input starts with a number T and then follows T lines contains a single number, N.

Output:
Find the total number of pairs, and print the required answer in a new line.

Constraints:
$1 \le T \le 10^5$
$1 \le N \le 10^7$