You are given an integer $n$.

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

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 $n$ ($1\leq n\leq 10^9$).

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 $-1$.

Note

In the third test case, $2^3 \cdot 3+3^2 \cdot 2 = 42$, so $(2,3),(3,2)$ will be considered as legal solutions.

In the fourth test case, $5^5 \cdot 5+5^5 \cdot 5 = 31250$, so $(5,5)$ is a legal solution.

Samples

5
3
7
42
31250
20732790

-1
-1
2 3
5 5
3 13