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 starts with a number $$T$$ and then follows $$T$$ lines contains a single number, $$N$$.
Find the total number of pairs, and print the required answer in a new line.
$$1 \le T \le 10^5$$
$$1 \le N \le 10^7$$
For 1st test case, pairs are (1,2) and (2,1)
For 2nd test case, pairs are (1,6) , (6,1) , (2,3) and (3,2).