Nasty Numbers

A positive integer is called nasty if it has at least two pairs of positive-integer factors such that the difference of one pair equals the sum of the other pair.

For example, 6 is nasty because $6 = 6 \times 1 = 2 \times 3$ and $6 - 1 = 2 + 3 = 5$. Similarly, 24 is nasty because $24 = 12 \times 2 = 6 \times 4$ and $12 - 2 = 6 + 4 = 10$.

Given a list of positive integers, determine for each one whether it is nasty.

The first line contains an integer $T$ ($T \le 20$), the number of integers to test. Each of the following $T$ lines contains one positive integer less than $32001$.

Print one line for each test value. After the value, print a space followed by is nasty if the value is nasty, or is not nasty otherwise. Keep the same order as the input.