### Task
The __dot product__ is usually encountered in linear algebra or scientific computing. It's also called __scalar product__ or __inner product__ sometimes:

> In mathematics, the __dot product__, or __scalar product__ (or sometimes __inner product__ in the context of Euclidean space), is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. [Wikipedia](https://en.wikipedia.org/w/index.php?title=Dot_product&oldid=629717691)

In our case, we define the dot product algebraically for two vectors `a = [a1, a2, …, an]`, `b = [b1, b2, …, bn]` as 
    
    dot a b = a1 * b1 + a2 * b2 + … + an * bn.
Your task is to find permutations of `a` and `b`, such that `dot a b` is minimal, and return that value. For example, the dot product of `[1,2,3]` and `[4,0,1]` is minimal if we switch `0` and `1` in the second vector.

### Examples
```python
min_dot([1,2,3,4,5], [0,1,1,1,0] ) = 6
min_dot([1,2,3,4,5], [0,0,1,1,-4]) = -17
min_dot([1,3,5]    , [4,-2,1]    ) = -3
```

### Remarks
If the list or array is empty, `minDot` should return 0. All arrays or lists will have the same length. Also, for the dynamically typed languages, all inputs will be valid lists or arrays, you don't need to check for `undefined`, `null` etc.

Note: This kata is inspired by [GCJ 2008](https://code.google.com/codejam/contest/32016/dashboard#s=p0).

```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 min_dot(a, b):\n    return sum((ai * bi) for ai, bi in zip(sorted(a), sorted(b, reverse=True)))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'min_dot'
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: 5826