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## ARIORGEO - Arithmetic or Geometric ?

Given a sequence of three real numbers, write a program that determine whether the sequence is part of an arithmetic progression or a geometric progression or neither of them.

Recall that an arithmetic progression of n terms with common difference “d” can be written in the form: a, a+d, a+2d, a+3d, ..., a+(n-1)d

and that a geometric progression of n terms with common ratio “r” can be written in the form: a, ar, ar2, ar3, ..., arn-1

### Input

The first line of the input contains an integer denoting the number of test cases. The description of test cases follows. Each test case is described in a single line containing three space-separated double precision real numbers.

### Output

For each test case, output a single line containing either:

• “Arithmetic”: if the numbers form an arithmetic progression.
•  “Geometric”: if the numbers form a geometric progression.
• “None”: if the numbers do not form any of them.
• “Both”: if the numbers form both of them.

### Example

```Input:
64 10 16-4 2 -11 4 100.5 -0.25 0.125-1.5 -0.5 0.52.18 2.18 2.18

Output:
ArithmeticGeometricNoneGeometricArithmeticBoth```

 Added by: mbk_live Date: 2019-01-09 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: C-CLANG C C++ 4.3.2 CPP CPP14 CPP14-CLANG C99 JAVA PYTHON PYTHON3 SWIFT