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CSES Problem Set

Counting Divisors


Task | Statistics


CSES - Counting DivisorsCSES - Counting Divisors

Time limit:1.00 s Memory limit:512 MB

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
Example

Input:
3
16
17
18


Output:
5
2
6