題目描述

You are given an integer $n$.

Find any pair of integers $(x,y)$ $(1 \leq x,y \leq n)$ such that $x^y y+y^x x=n$.

輸入格式

The first line contains a single integer $t$ $(1 \leq t \leq 10^4)$ — the number of test cases. Each test case contains one line with a single integer $n$ $(1 \leq n \leq 10^{18})$.

輸出格式

For each test case, if possible, print two integers $x$ and $y$ $(1 \leq x,y \leq n)$. If there are multiple answers, print any. Otherwise, print $-1$ .

Samples

5
3
7
42
31250
20732790

-1
-1
2 3
5 5
3 13

原始資料

• Zero1 題號：a950
• Hydro 題號：Z0950
• Locale：zh_TW
• Display：open