# 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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def sum_of_regular_numbers(arr):\n    # (step size, step count, sequence base)\n    grouped = [(b - a, 1, a) for a, b in zip(arr[:-1], arr[1:])]\n    # Collate the groups by step size\n    i = 0\n    while i < len(grouped) - 1:\n        if grouped[i][0] == grouped[i + 1][0]:\n            grouped[i] = (grouped[i][0], grouped[i][1] + 1, grouped[i][2])\n            del grouped[i + 1]\n        else:\n            i += 1\n    # Use (first + last) * elements / 2 to find sum of each sequence longer than 2 elements long\n    return sum((2 * base + step * steps) * ((steps + 1) / 2) for step, steps, base in grouped if steps >= 2)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sum_of_regular_numbers'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 7110