Number of divisors for many numbers

For each given integer n, you are asked to find the number of divisors of n.

Input

The first line of the input contains a single integer t (2 ≤ n ≤ 1000) the number of test cases.
The next t lines contain t integers (1 ≤ ).

Output

The program should print the number of divisors for each on a separate line.

Examples

Input
Output
3 8 23 74
4 2 4
 

Constraints

Time limit: 3 seconds

Memory limit: 512 MB

Output limit: 1 MB

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