Description:
Gregor is learning about RSA cryptography, and although he doesn't understand how RSA works, he is now fascinated with prime numbers and factoring them.
Gregor's favorite prime number is $$$P$$$. Gregor wants to find two bases of $$$P$$$. Formally, Gregor is looking for two integers $$$a$$$ and $$$b$$$ which satisfy both of the following properties.
- $$$P \bmod a = P \bmod b$$$, where $$$x \bmod y$$$ denotes the remainder when $$$x$$$ is divided by $$$y$$$, and
- $$$2 \le a < b \le P$$$.
Help Gregor find two bases of his favorite prime number!
Input Format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$).
Each subsequent line contains the integer $$$P$$$ ($$$5 \le P \le {10}^9$$$), with $$$P$$$ guaranteed to be prime.
Output Format:
Your output should consist of $$$t$$$ lines. Each line should consist of two integers $$$a$$$ and $$$b$$$ ($$$2 \le a < b \le P$$$). If there are multiple possible solutions, print any.
Note:
The first query is $$$P=17$$$. $$$a=3$$$ and $$$b=5$$$ are valid bases in this case, because $$$17 \bmod 3 = 17 \bmod 5 = 2$$$. There are other pairs which work as well.
In the second query, with $$$P=5$$$, the only solution is $$$a=2$$$ and $$$b=4$$$.