Karan's company makes software that provides different features based on the version of operating system of the user.

For finding which version is more recent, Karan uses the following method:

While this function worked for OS versions 10.6, 10.7, 10.8 and 10.9, the Operating system company just released OS version 10.10.

Karan's function fails for the new version:

```python
compare_versions ("10.9", "10.10");       # returns True, while it should return False
```

Karan now wants to spend some time to right a more robust version comparison function that works for any future version/sub-version updates.

Help Karan write this function. Here are a few sample cases:

```python
compare_versions("11", "10");                    # returns True
compare_versions("11", "11");                    # returns True
compare_versions("10.4.6", "10.4");              # returns True
compare_versions("10.4", "11");                  # returns False
compare_versions("10.4", "10.10");               # returns False
compare_versions("10.4.9", "10.5");              # returns False
```
```haskell  
compareVersions "11" "10"       `shouldBe` GT
compareVersions "10.4.6" "10.4" `shouldBe` GT
compareVersions "10.10" "10.9"  `shouldBe` GT
compareVersions xs xs           `shouldBe` EQ -- xs is an arbitrary version
compareVersions "10" "11"         `shouldBe` LT
compareVersions "10.4" "10.4.6"   `shouldBe` LT
compareVersions "10.99" "10.100"  `shouldBe` LT
```

It can be assumed that version strings are non empty and only contain numeric literals and the character `'.'`.

```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 compare_versions(version1, version2):\n    v1 = version1.split('.')\n    v2 = version2.split('.')\n    a = max(len(v1), len(v2))\n    v1.append('0'*abs(len(v1) - a))\n    v2.append('0'*abs(len(v2) - a))\n    if v1[-1] == '':\n        v1.pop(-1)\n    if v2[-1] == '':\n        v2.pop(-1)\n    k = 0\n    for i in v1:\n        if int(i) < int(v2[k]):\n            return False\n        elif int(i) >= int(v2[k]):\n            k += 1\n    return True"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'compare_versions'
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: 6072