You have n  tiles, where each tile has one letter tiles[i] printed on it.
Return the number of possible non-empty sequences of letters you can make using the letters printed on those tiles.
 
Example 1:
Input: tiles = "AAB"
Output: 8
Explanation: The possible sequences are "A", "B", "AA", "AB", "BA", "AAB", "ABA", "BAA".

Example 2:
Input: tiles = "AAABBC"
Output: 188

Example 3:
Input: tiles = "V"
Output: 1

 
Constraints:

1 <= tiles.length <= 7
tiles consists of uppercase English letters.

```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 = "# This is a mathematical problem.\n# Get the frequencies of different characters [f_0, f_1, ..., f_n].\n# For each possible choice of frequency [i_0, i_1, ..., i_n] (0 <= i_k <= f_k, k = 0, 1, ..., n),\n# the number of distinct sequences is (i_0 + i_1 + ... + i_n)! / ( i_0! * i_1! * ... * i_n!).\n\n# To get numbers of occurrences you can just run\n\n#         freq = count.values()\n# for this problem you only need to iterate over freq, so you don't even need to convert it to list.\n# Kind of depends on your taste, but for calculating digits you have the option of using divmod:\n\n#             for f in freq:\n#                 i, mod = divmod(i, f + 1)\n#                 digits.append(mod)\n\n\n\nimport collections, math\nclass Solution:\n    def numTilePossibilities(self, tiles: str) -> int:\n        freq = collections.Counter(tiles)\n        prod = 1\n        for f in freq.values():\n            prod *= f + 1\n        res = 0\n        for i in range(1, prod):\n            digits = []\n            for f in freq.values():\n                digits.append(i % (f + 1))\n                i = i // (f + 1)\n            tmp = math.factorial(sum(digits))\n            for d in digits:\n                tmp //= math.factorial(d)\n            res += tmp\n        return res"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numTilePossibilities'
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: 9900