You are given three integers in the range [0-99]. You must determine if any ordering of the numbers forms a date from the 20th century.

- If no ordering forms a date, return the string `"invalid"`.

- If multiple distinct orderings form dates, return the string `"ambiguous"`.

- If only one ordering forms a date, return that date as a string with format `"YY/MM/DD"`.

## Examples

```python
unique_date(13, 12, 77) == '77/12/13' # only the ordering (77, 12, 13) forms a date
unique_date(13, 77, 12) == '77/12/13' # argument order is irrelevant

unique_date(1, 2, 3) == 'ambiguous' # 01/02/03, 02/01/03, ...
unique_date(3, 2, 1) == 'ambiguous'

unique_date(50, 40, 60) == 'invalid' # no ordering could form a date
unique_date(40, 50, 60) == 'invalid'
```

## Note
This kata was inspired by my encounter with [google.com/foobar](http://www.google.com/foobar)

```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 datetime import datetime\nfrom itertools import permutations\n\ndef unique_date(*args):\n    dates = set()\n    for p in permutations(args):\n        try:\n            date = \'{:02}/{:02}/{:02}\'.format(*p)\n            datetime.strptime(date, \'%y/%m/%d\')\n            dates.add(date)\n        except ValueError: pass\n    return dates.pop() if len(dates) == 1 else "ambiguous" if dates else "invalid"'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'unique_date'
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: 428352