Given $n$ integers, your task is to report for each integer the number of its divisors.

For example, if $x=18$, the correct answer is $6$ because its divisors are $1,2,3,6,9,18$.

Input

The first input line has an integer $n$: the number of integers.

After this, there are $n$ lines, each containing an integer $x$.

Output

For each integer, print the number of its divisors.

Constraints

• $1 \le n \le 10^5$
• $1 \le x \le 10^6$

Example

Input:

3
16
17
18

Output:

5
2
6