# Task
Given a number `n`, return a string representing it as a sum of distinct powers of three, or return `"Impossible"` if that's not possible to achieve.


# Input/Output


`[input]` integer `n`


A positive integer n. 

`1 ≤ n ≤ 10^16`.

`[output]` a string

A string representing the sum of powers of three which adds up to n, or `"Impossible"` if there is no solution. If the solution does exist, it should be return as `"3^a1+3^a2+ ... +3^an"`, where ai for `0 ≤ i ≤ n` represents the corresponding exponent of the term. The terms in the string should also be sorted in descending order, meaning that higher powers should appear before the lower ones in the string (`"3^0+3^1"` is incorrect, whereas `"3^1+3^0"` is correct).

# Example

For `n = 4`, the output should be `"3^1+3^0"`.

4 can be represented as `3+1` which is in fact 3 to the power of 1 plus 3 to the power of 0

For `n = 2`, the output should be `"Impossible"`.

There is no way to represent 2 as a sum of `distinct powers` of 3.

```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 = "from bisect import bisect\n\ndef sum_of_threes(n, xs=[3**i for i in range(34)]):\n    result = []\n    while n >= 1:\n        x = bisect(xs, n) - 1\n        n -= 3 ** x\n        result.append(x)\n    return 'Impossible' if len(result) != len(set(result)) else '+'.join(f'3^{x}' for x in result)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sum_of_threes'
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: 5976