a950. Exponential Equation - Zero1 Online Judge System

Content

You are given an integer $n$.

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

Input

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 $n$ $(1 \leq n \leq 10^{18})$.

Output

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 $-1$ .

Sample Input #1

Sample Output #1

測資資訊：

記憶體限制： 64 MB
不公開測資點#0 (8%): 1.0s , <1K
不公開測資點#1 (8%): 1.0s , <1K
不公開測資點#2 (8%): 1.0s , <1K
不公開測資點#3 (8%): 1.0s , <1K
不公開測資點#4 (8%): 1.0s , <1K
不公開測資點#5 (8%): 1.0s , <1K
不公開測資點#6 (8%): 1.0s , <1M
不公開測資點#7 (8%): 1.0s , <1M
不公開測資點#8 (9%): 1.0s , <1M
不公開測資點#9 (9%): 1.0s , <1M
不公開測資點#10 (9%): 1.0s , <1M
不公開測資點#11 (9%): 1.0s , <1M

Hint ：

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出處:

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1164120-7@g.... (hcng)

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