In mathematics, a [Diophantine equation](https://en.wikipedia.org/wiki/Diophantine_equation) is a polynomial equation, usually with two or more unknowns, such that only the integer solutions are sought or studied.

In this kata we want to find all integers `x, y` (`x >= 0, y >= 0`) solutions of a diophantine equation of the form:
#### x^(2) - 4 \* y^(2) = n

(where the unknowns are `x` and `y`, and `n` is a given positive number)
in decreasing order of the positive xi. 

If there is no solution return `[]` or `"[]" or ""`. (See "RUN SAMPLE TESTS" for examples of returns).


## Examples:

```
solEquaStr(90005) --> "[[45003, 22501], [9003, 4499], [981, 467], [309, 37]]"
solEquaStr(90002) --> "[]"
```

## Hint:

x^(2) - 4 \* y^(2) = (x - 2\*y) \* (x + 2\*y)

```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 sol_equa(n):\n  # x^2 - 4y^2 = n -> return [x, y]\n  # Factor to n = (x+2y)(x-2y)\n  solutions, i = [], 1\n  while i*i <= n:\n    if n % i == 0: # Factor found: (j=n//i: so: i*j = n)\n      j = n // i\n      if (i+j) % 2 == 0:  # (x + 2y)+(x - 2y)    = (2x)\n        # Fits requirements for x!!!\n        x = (i+j)//2      # (i      + j )    / 2 =  x\n        v, V = i-x, j-x   # (i  - x = 2y) and (j - x = -2y)\n        if v % 2 == 0 and v == V * -1:\n          # Fits requirements for y!!!\n          y = abs(v//2)\n          solutions.append([x, y])\n    i += 1\n  return solutions\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sol_equa'
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: 5686