13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T7a8,

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
$$$2 \le a \lt b \le P$$$.

Help Gregor find two bases of his favorite prime number!

Input

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

Gregor and Cryptography

Examples