Our AAA company is in need of some software to help with logistics: you will be given the width and height of a map, a list of x coordinates and a list of y coordinates of the supply points, starting to count from the top left corner of the map as 0.

Your goal is to return a two dimensional array/list with every item having the value of the distance of the square itself from the closest supply point expressed as a simple integer.

Quick examples:

```python
logistic_map(3,3,[0],[0])
#returns
#[[0,1,2],
# [1,2,3],
# [2,3,4]]
logistic_map(5,2,[0,4],[0,0])
#returns
#[[0,1,2,1,0],
# [1,2,3,2,1]]
```

Remember that our company is operating with trucks, not drones, so you can simply use Manhattan distance. If supply points are present, they are going to be within the boundaries of the map; if no supply point is present on the map, just return `None`/`nil`/`null` in every cell.

```python
logistic_map(2,2,[],[])
#returns
#[[None,None],
# [None,None]]
```

**Note:** this one is taken (and a bit complicated) from a problem a real world AAA company [whose name I won't tell here] used in their interview. It was done by a friend of mine. It is nothing that difficult and I assume it is their own version of the FizzBuzz problem, but consider candidates were given about 30 mins to solve it.

```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 logistic_map(width, height, xs, ys):\n    neighbours = lambda c: {(c[0] + i, c[1] + j)\n                    for i, j in [(0, 1), (1, 0), (0, -1), (-1, 0)]\n                        if 0 <= c[0] + i < width and 0 <= c[1] + j < height}\n    grid = [[None] * width for _ in range(height)]\n    distance, seen, bag = 0, set(), set(zip(xs, ys))\n    while bag:\n        for x, y in bag:\n            grid[y][x] = distance\n        seen |= bag\n        bag = set.union(*map(neighbours, bag)) - seen\n        distance += 1\n    return grid'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'logistic_map'
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: 9090