**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

- 1 \le n \le 10^5
- 1 \le x \le 10^6

# Example

Input:

3 16 17 18

Output:

5 2 6