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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:
6
4 10 16
-4 2 -1
1 4 10
0.5 -0.25 0.125
-1.5 -0.5 0.5
2.18 2.18 2.18
Output: Arithmetic
Geometric
None
Geometric
Arithmetic
Both

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

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