Given a positive integer N, what is the minimum positive integer K such that K! is a multiple of the square of N!?</p>

Note that a is a multiple of b if a = b · k for some integer k.

Moreover, note that for any positive integer M, M! is the product of all positive integers whose value is at most M.

입력 형식

The first line of input contains T, the number of test cases. The following lines describe the test cases.</p>

Each test case consists of one line containing a single integer, N.

Constraints

• 1 ≤ T ≤ 200000
• 1 ≤ N ≤ 200000

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

예제 입력

5
4
5
7
11
24

예제 출력

8
10
14
22
48