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Linear Sequence

Statement

 Goal

WHAT IS LINEAR SEQUENCE?

A linear sequence is a number pattern that increases or decreases by the same amount each time. (From BBC Bitesize: https://www.bbc.co.uk/bitesize/guides/z7j2pv4/revision/)

The nth term can be found using the formula:
nth term = first term of the sequence + (n - 1) * common difference

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YOUR TASK

You will be given four integers, a, b, c and d, each representing the first, second, third and forth term of the sequence. You need to determine whether they are in a linear sequence.

If they are in a linear sequence, you need to find the formula to find the nth term of the sequence, in the form of xn+y or xn-y. The nth term is 1-indexed, i.e. the indexes of the first four terms are 1, 2, 3, 4.

In this task, x and y are non-zero. However, x can be -1 or 1 so you will need to simplify the formula as follows:
 1n+y →  n+y
-1n+y → -n+y


If the numbers provided are not a linear sequence, output ERROR.
Input
Lines 1 to 4: a, b, c and d: integers, each on a separate line.
Output
Line 1: Output a formula in the form of xn+y or xn-y or ERROR
Constraints
-100 < a, b, c and d < 5201315
x and y are always integers.
x, y ≠ 0
Example
Input
15
20
25
30
Output
5n+10

Game modes
Fastest, Shortest, Reverse

Test cases
Example Test
Input
15 20 25 30
Output
5n+10

Validator 1 Validator
Input
10 19 28 37
Output
9n+1

Bigger Number, both x and y are positive. Test
Input
32 43 54 65
Output
11n+21

Validator 2 Validator
Input
35 40 45 50
Output
5n+30

x is negative Test
Input
65 50 35 20
Output
-15n+80

Validator 3 Validator
Input
32 28 24 20
Output
-4n+36

y is negative Test
Input
-8 -4 0 4
Output
4n-12

Validator 4 Validator
Input
-9 -5 -1 3
Output
4n-13

both x and y are negative Test
Input
-9 -13 -17 -21
Output
-4n-5

Validator 5 Validator
Input
-32 -38 -44 -50
Output
-6n-26

x is 1 Test
Input
10 11 12 13
Output
n+9

Validator 6 Validator
Input
3 4 5 6
Output
n+2

x is -1 Test
Input
6 5 4 3
Output
-n+7

Validator 7 Validator
Input
-9 -10 -11 -12
Output
-n-8

ERROR Test
Input
69 420 5201314 69
Output
ERROR

Validator 8 Validator
Input
8 9 5 6
Output
ERROR

Solution language

Solution

Stub generator input