Pretty new to programming, been doing some pretty basic stuff but I came across a more complicated one now (C language), not sure how to start with it. I’m not understanding the definition of “*K*! is a multiple of the square of *N*” to be frank, so I can’t really tell what is expected from me here. If anyone could just explain the point to me, I would really appreciate it.

Task:

Given a positive integer

N, what is the minimum positive integerKsuch thatK! is a multiple of the square ofN?Note that

ais a multiple ofbifa=b*kfor some integerk.

Moreover, note that for any positive integerM, M! is the product of all positive integers whose value is at mostM.Input:

The first line of input contains

T, the number of test cases. The following lines describe the test cases.

Each test case consists of one line containing a single integerN.Output:

For each test case, print a single integer which is the answer for that test case.

Constraints:

1 <= T <= 200000

1 <= N <= 200000Sample Input:

5

4

5

7

11

24Sample Output:

8

10

14

22

48

Thanks a lot in advance for any tips!