Bablu is very fond of Series and Sequences...

After studying Fibonacci Series in Class IX, he was impressed and he designed his own sequence as follows...

a[0] = a[1] = 0 

For n > 1, a[n] = a[n - 1] + f(n), where f(n) is smallest prime factor of n.

He is also very fond of programming and thus made a small program to find a[n], but since he is in Class IX, he is not very good at programming. So, he asks you for help. Your task is to find a[n] for the above sequence....

Input

Your code will be checked for multiple test cases.

First line of Input contains T (≤ 100), the number of test cases.

Next T lines contain a single number N. (1 < N < 10⁷).

Output

Single line containing a[n] i.e. nth number of the sequence for each test case.

Example

Input:
3
2
3
4

Output:
2
5
7