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Points:
4

Time limit:
2.0s

Memory limit:
256M

Author:

Problem type

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Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, ~~CommonLisp~~, D, Dart, F#, Forth, Fortran, Go, ~~Groovy~~, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, ~~Nim~~, ~~ObjC~~, OCaml, ~~Octave~~, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

kushanzaveri loves sequences. However, he finds that the grade 11 categorizations of sequences are too easy.

Sequences have 4 categories:

- Arithmetic: Consecutive terms have a constant difference.
- Geometric: Consecutive terms have a constant factor (multiple)
- Both: Both an arithmetic and geometric sequence
- Random: Not an arithmetic nor geometric sequence

kushanzaveri says:

Categorizing a sequence is an easy P1 of a contest

#### Input Specification

Input will initiate with a single integer , the number of elements in the sequence.

The second line will contain integers, , the ^{th} element. .

#### Output Specification

`arithmetic`

, `geometric`

, `both`

, or `random`

depending on the type of sequence.

#### Sample Input 1

```
4
1 3 9 27
```

#### Sample Output 1

`geometric`

#### Sample Input 2

```
5
-1 2 -3 4 -5
```

#### Sample Output 2

`random`

## Comments

Does anyone know what Test Case #3 is? I got all AC except for that one.

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It depends on definition but it is