### What is simplifying a square root?

If you have a number, like 80, for example, you would start by finding the greatest perfect square divisible by 80. In this case, that's 16. Find the square root of 16, and multiply it by 80 / 16. Answer = 4 √5. 

##### The above example:

![simplify_roots_example.png](https://i.postimg.cc/gjv2NwCm/simplify-roots-example.png)

### Task:

Your job is to write two functions, `simplify`, and `desimplify`, that simplify and desimplify square roots, respectively. (Desimplify isn't a word, but I couldn't come up with a better way to put it.) `simplify` will take an integer and return a string like "x sqrt y", and `desimplify` will take a string like "x sqrt y" and return an integer. For `simplify`, if a square root cannot be simplified, return "sqrt y". 

_Do not modify the input._

### Some examples:

```python
simplify(1)  #=> "1"
simplify(2)  #=> "sqrt 2"
simplify(3)  #=> "sqrt 3"
simplify(8)  #=> "2 sqrt 2"
simplify(15) #=> "sqrt 15"
simplify(16) #=> "4"
simplify(18) #=> "3 sqrt 2"
simplify(20) #=> "2 sqrt 5"
simplify(24) #=> "2 sqrt 6"
simplify(32) #=> "4 sqrt 2"

desimplify("1")        #=> 1
desimplify("sqrt 2")   #=> 2
desimplify("sqrt 3")   #=> 3
desimplify("2 sqrt 2") #=> 8
desimplify("sqrt 15")  #=> 15
desimplify("4")        #=> 16
desimplify("3 sqrt 2") #=> 18
desimplify("2 sqrt 5") #=> 20
desimplify("2 sqrt 6") #=> 24
desimplify("4 sqrt 2") #=> 32
```

Also check out my other creations — [Square Roots: Approximation](https://www.codewars.com/kata/square-roots-approximation), [Square and Cubic Factors](https://www.codewars.com/kata/square-and-cubic-factors), [Keep the Order](https://www.codewars.com/kata/keep-the-order), [Naming Files](https://www.codewars.com/kata/naming-files), [Elections: Weighted Average](https://www.codewars.com/kata/elections-weighted-average), [Identify Case](https://www.codewars.com/kata/identify-case), [Split Without Loss](https://www.codewars.com/kata/split-without-loss), [Adding Fractions](https://www.codewars.com/kata/adding-fractions),
[Random Integers](https://www.codewars.com/kata/random-integers), [Implement String#transpose](https://www.codewars.com/kata/implement-string-number-transpose), [Implement Array#transpose!](https://www.codewars.com/kata/implement-array-number-transpose), [Arrays and Procs #1](https://www.codewars.com/kata/arrays-and-procs-number-1), and [Arrays and Procs #2](https://www.codewars.com/kata/arrays-and-procs-number-2).

```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 = "import re\nfrom collections import Counter\n\ndef prime_factor(n):\n    if n == 1:\n        return Counter([1])\n    factors = Counter()\n    for i in range(2, int(n ** 0.5) + 1):\n        while n % i == 0:\n            factors[i] += 1\n            n //= i\n    if n != 1:\n        factors[n] = 1\n    return factors\n\n\ndef simplify(n):\n    a, b = 1, 1\n    for k, v in prime_factor(n).items():\n        while v >= 2:\n            a *= k\n            v -= 2\n        b = b * k if v else b\n    if a == 1:\n        return f'sqrt {b}' if b > 1 else '1'\n    if b == 1:\n        return str(a)\n    return f'{a} sqrt {b}'\n\n\ndef desimplify(s):\n    res = re.match(r'(\\d+ ?)?(sqrt (\\d+))?', s)\n    a, b = res.group(1), res.group(3)\n    ans = int(a)**2 if a else 1\n    return ans * int(b) if b else ans"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'simplify'
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: 10202