The pair of integer numbers `(m, n)`, such that `10 > m > n > 0`,  (below 10), that its sum, `(m + n)`, and rest, `(m - n)`, are perfect squares, is (5, 4).

Let's see what we have explained with numbers.
```
5 + 4 = 9 = 3²
5 - 4 = 1 = 1²
(10 > 5 > 4 > 0)
```

The pair of numbers `(m, n)`, closest to and below 50, having the property described above is `(45, 36)`.
```
45 + 36 = 81 = 9²
45 - 36 = 9 = 3²
(50 > 45 > 36 > 0)
```

With the function `closest_pair_tonum()`, that receives a number `upper_limit`, as an upper limit, we should be able to obtain the closest pair to `upper_limit`, that fulfills the property described above.

The function should return the largest pair of numbers `(m, n)`, satisfying `upper_limit > m > n > 0`. Note that we say pair A `(a0, a1)` is larger than pair B `(b0, b1)` when `a0 > b0` or `a0 == b0 and
a1 > b1`.

Let's see some cases:

```python
closest_pair_tonum(10) == (5, 4) # (m = 5, n = 4)

closest_pair_tonum(30) == (29, 20)

closest_pair_tonum(50) == (45, 36)
```

Happy coding and enjoy it!!
(We will be having a second part of a similar exercise (in some days) that will need a faster algorithm for values of `upper_limit` < 1000)

```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 closest_pair_tonum(lim):\n    return next((m, n) for m in range(lim-1, 0, -1) for n in range(m-1, 0, -1) if not ((m+n)**0.5%1 or (m-n)**0.5%1))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'closest_pair_tonum'
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: 5796