Messy Room#12212
BMO found labubus under his bed while he was cleaning his messy room. He wants to organize them and put them in exactly one rectangular grid.
Fortunately, he has all possible rectangular grids with integer sides greater than . In other words, he has all rectangles with sides such that are integers and a,b \ge 2.
He wants your help to find the smallest rectangular grid that could fit the toys in different scenarios.
A rectangular grid is considered to be smaller than a rectangular grid if \operatorname{Area}(A) \le \operatorname{Area}(B).
A rectangular grid is said to fit toys if \operatorname{Area}(A) \ge n.
Each test contains multiple test cases. The first line contains a single integer (1 \le t \le 1000)—the number of test cases.
Each test case consists of only one number (3 \le n \le 1000)—the number of toys.
For each test case, output a single integer: the area of the smallest rectangular grid that could fit all toys.
Example 1
In the first test case, BMO can put the toys in a by rectangular grid. It can be shown that there is no smaller rectangular grid that could fit the toys.
In the second test case, BMO can put the toys in a by rectangular grid. It can be shown that there is no smaller rectangular grid that could fit the toys.
Subtask ( points): is even
Subtask ( points): is a multiple of
Subtask ( points): No additional constraints