Task

You are given a regular array arr. Let's call a step the difference between two adjacent elements.

Your task is to sum the elements which belong to the sequence of consecutive elements of length at least 3 (but as long as possible), such that the steps between the elements in this sequence are the same.

Note that some elements belong to two sequences and have to be counted twice.

Example

For arr = [54, 70, 86, 1, -2, -5, 0, 5, 78, 145, 212, 15], the output should be 639.

There are 4 sequences of equal steps in the given array:
{54, 70, 86} => step +16
{1, -2, -5} => step -3
{-5, 0, 5} => step +5
{78, 145, 212} => step +67
So the answer is 
(54 + 70 + 86) + 
(1 - 2 - 5) + 
(-5 + 0 + 5) + 
(78 + 145 + 212) = 639.
The last element 15 was not be counted.

For arr = [7, 2, 3, 2, -2, 400, 802], the output should be 1200.

There is only 1 sequence in arr:
{-2, 400, 802} => step +402
So the answer is: -2 + 400 + 802 = 1200

For arr = [1, 2, 3, 4, 5], the output should be 15.

Note that we should only count {1, 2, 3, 4, 5} as a whole, any other small subset such as {1, 2, 3},{2, 3, 4},{3, 4, 5} are belong to {1, 2, 3, 4, 5}.

Input/Output

• [input] array.integer arr

3 ≤ arr.length ≤ 100

• [output] an integer

The sum of sequences.