My little sister came back home from school with the following task:
given a squared sheet of paper she has to cut it in pieces
which, when assembled, give squares the sides of which form
an increasing sequence of numbers.
At the beginning it was lot of fun but little by little we were tired of seeing the pile of torn paper.
So we decided to write a program that could help us and protects trees.

## Task

Given a positive integral number n, return a **strictly increasing** sequence (list/array/string depending on the language) of numbers, so that the sum of the squares is equal to n².

If there are multiple solutions (and there will be), return as far as possible the result with the largest possible values:

## Examples

`decompose(11)` must return `[1,2,4,10]`. Note that there are actually two ways to decompose 11²,
11² = 121 = 1 + 4 + 16 + 100 = 1² + 2² + 4² + 10² but don't return `[2,6,9]`, since 9 is smaller than 10.

For `decompose(50)` don't return `[1, 1, 4, 9, 49]` but `[1, 3, 5, 8, 49]` since `[1, 1, 4, 9, 49]`
doesn't form a strictly increasing sequence.

## Note
Neither `[n]` nor `[1,1,1,…,1]` are valid solutions. If no valid solution exists, return `nil`, `null`, `Nothing`, `None` (depending on the language) or `"[]"` (C) ,`{}` (C++), `[]` (Swift, Go).

The function "decompose" will take a positive integer n 
and return the decomposition of N = n² as:

- [x1 ... xk]
or
- "x1 ... xk"
or
- Just [x1 ... xk]
or
- Some [x1 ... xk]
or
- {x1 ... xk}
or
- "[x1,x2, ... ,xk]"

depending on the language (see "Sample tests")

# Note for Bash
```
decompose 50 returns "1,3,5,8,49"
decompose 4  returns "Nothing"
```
# Hint

Very often `xk` will be `n-1`.

```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 math\ndef decompose(n):\n    value = n-1\n    remains = n**2\n    cache = {value : remains}\n    remains -= value**2\n    \n    while remains:\n        value = int(math.sqrt(remains))\n        if value < min(cache.keys()):\n            cache[value] = remains\n            remains -= value**2\n        else:\n            del cache[min(cache.keys())]\n            if not cache: return None\n            value = min(cache.keys())\n            remains = cache.pop(value)\n            cache[value-1] = remains\n            remains -= (value-1)**2\n    return sorted(cache.keys())'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'decompose'
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: 5962