Is this an arithmetic progression?

Given 3 numbers a, b, and c your task is to determine if those 3 numbers could form an arithmetic progression. Print arithmetic progression in case those 3 numbers could be part of an arithmetic progression and no pattern found otherwise.

Definition of an Arithmetic Progression

An arithmetic progression is a sequence of numbers where each term is obtained by adding a fixed number to the previous term. For example, -4, -2, 0, 2, 4 is an arithmetic progression because each term is obtained by adding 2 to the previous term (-4 + 2 = -2, -2 + 2 = 0, and so on).

Input

Output

1 2 3

arithmetic progression

1 2 2

no pattern found

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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