In this Kata, you will implement the [Luhn Algorithm](http://en.wikipedia.org/wiki/Luhn_algorithm), which is used to help validate credit card numbers.

Given a positive integer of up to 16 digits, return ```true``` if it is a valid credit card number, and ```false``` if it is not.

Here is the algorithm:
  
* Double every other digit, scanning **from right to left**, starting from the second digit (from the right).

  Another way to think about it is: if there are an **even** number of digits, double every other digit starting with the **first**; if there are an **odd** number of digits, double every other digit starting with the **second**:

  ```
  1714 ==> [1*, 7, 1*, 4] ==> [2, 7, 2, 4]
  
  12345 ==> [1, 2*, 3, 4*, 5] ==> [1, 4, 3, 8, 5]
  
  891 ==> [8, 9*, 1] ==> [8, 18, 1]
  ```

*  If a resulting number is greater than `9`, replace it with the sum of its own digits (which is the same as subtracting `9` from it):

  ```
  [8, 18*, 1] ==> [8, (1+8), 1] ==> [8, 9, 1]
  
  or:
  
  [8, 18*, 1] ==> [8, (18-9), 1] ==> [8, 9, 1]
  ```
  
* Sum all of the final digits:

  ```
  [8, 9, 1] ==> 8 + 9 + 1 = 18
  ```

* Finally, take that sum and divide it by `10`.  If the remainder equals zero, the original credit card number is valid.
    ```
    18 (modulus) 10 ==> 8 , which is not equal to 0, so this is not a valid credit card number
    ```

```if:fsharp,csharp
For F# and C# users:

The input will be a string of spaces and digits `0..9`

```

```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 validate(n):\n    digits = [int(x) for x in str(n)]\n    even = [x*2 if x*2 <= 9 else x*2 - 9 for x in digits[-2::-2]]\n    odd  = [x for x in digits[-1::-2]]\n    return (sum(even + odd)%10) == 0\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'validate'
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: 5734