Description

Yi Chan wants to know how strong the “fate” between him and his master is. But how can it be measured?

Yi Chan comes up with an idea. First, he and his master agree on a positive integer $n$. Then each of them silently thinks of a positive integer not greater than $n$.

Yi Chan believes that the larger the least common multiple of these two numbers is, the stronger the fate between him and his master is.

His master thinks this method is good, but he wants to know what the maximum possible least common multiple of the two numbers can be.

His master is not very good at math, so he asks Yi Chan. Yi Chan also finds this problem difficult, and he hopes you can tell him the answer.

Input Format

This problem contains multiple test cases.

The first line contains a positive integer $T$, the number of test cases.

The next $T$ lines each contain a positive integer $n$, the positive integer agreed upon by Yi Chan and his master.

Output Format

For each test case, output one positive integer per line, the answer.

1
3

6

Hint

[Sample $1$ Explanation]

Among two positive integers not greater than $3$, the maximum least common multiple is $\mathrm{lcm}(2,3) = 6$.

[Constraints]

For $50\%$ of the testdata, $1 \le T,n \le 100$.

For $100\%$ of the testdata, $1 \le T \le 100$, $1 \le n \le 10^9$.

Translated by ChatGPT 5