In a class the teacher gave all the acm icpc aspirants a challenge on number theory. They could not solve it so they need your help. Help the students to solve this task.

The task that you will be given a number N. You have to calculate the number of positive integral divisors of that number. 

(1 and N are considered to be the divisors of N)

Input

There are T test cases.(1≤T≤102).

First you will be given the number T. Then T numbers follow.

(numbers are space separated)

next line contains T numbers N (1 ≤ N ≤ 10^18).

Output

In each line print the number of divisors of a number N.

Example

Input:
3
6 24 100

Output:
4
8
9