A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: 

2332
110011
54322345

For a given number ```num```, return its closest numerical palindrome which can either be smaller or larger than ```num```. If there are 2 possible values, the larger value should be returned. If ```num``` is a numerical palindrome itself, return it. 

For this kata, single digit numbers will NOT be considered numerical palindromes. 

Also, you know the drill - be sure to return "Not valid" if the input is not an integer or is less than 0.

```
palindrome(8) => 11
palindrome(281) => 282 
palindrome(1029) => 1001
palindrome(1221) => 1221
palindrome("1221") => "Not valid"

```

```Haskell
In Haskell the function should return a Maybe Int with Nothing for cases where the argument is less than zero.
```
Other Kata in this Series:
Numerical Palindrome #1
Numerical Palindrome #1.5
Numerical Palindrome #2
Numerical Palindrome #3
Numerical Palindrome #3.5
Numerical Palindrome #4
Numerical Palindrome #5

```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 = '""" Solution without loops ! """\n\n""" Define the first segment of what wwould be a "not far away palindrome" based on "num" :\n            num = 1258  -> midPart = 12  ( -> would give "1221" )\n            num = 459   -> midPart = 45  ( -> would give "454"  )\n    \n    Check for lower and upper values (in case num is near of change of decade, upperbond or lowerbond)\n    and define 3 possible parts of palindromes:\n            num = 1258  -> 12  ->  lowPart  = 11\n                                   midPart  = 12\n                                   highPart = 13\n            num = 459   -> 45  ->  lowPart  = 44\n                                   midPart  = 45\n                                   highPart = 46\n                                   \n    Construct palindromes according to each part an the parity of the length of the original number:\n            num = 1258  -> lPal = 1111 ; mPal = 1221 ; hPal = 1331\n            num = 459   -> lPal = 444  ; mPal = 454  ; hPal = 464\n    \n    Sort the result with tuples defined as:     (abs(num-newPal), -newPal)\n    This way, the nearest new palindrome value are first, and if two values of "abs(num-newPal)"\n    are equal, the second element of the tuple ensure to find the highest one as first element of \n    the sorted list of tuples.\n    return the opposite of the second element of the first tuple, which is so "newPal".\n    \n    Edge cases:  num = 1999 -> lPal = 1881 ; mPal = 1991 ; hPal = 2002  =>  return 2002\n                 num = 801  -> lPal = 797  ; mPal = 808  ; hPal = 818   =>  return 797\n                 num = 1002 -> lPal = 99(!); mPal = 1001 ; hPal = 1111  =>  return 1001\n"""\n\ndef nextPal(sPart, ls): return int( sPart + sPart[:len(sPart)-ls%2][::-1] )\n\ndef palindrome(num):\n    if type(num) != int or num <= 0: return "Not valid"\n    \n    s = str(num)\n    midPart  = s[:(len(s)+1)//2]\n    lowPart  = str(int(midPart)-1)\n    highPart = str(int(midPart)+1)\n    lPal, mPal, hPal = nextPal(lowPart, len(s)), nextPal(midPart, len(s)), nextPal(highPart, len(s))\n    \n    return 11 if num <= 16 else -sorted( (abs(num-pal), -pal)  for pal in [lPal, mPal, hPal] )[0][1]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'palindrome'
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: 5926