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 = "class Solution:\n    def numTilePossibilities(self, tiles: str) -> int:\n        def next_permutation(a):\n            for i in range(len(a) - 1, 0, -1):\n                if a[i] > a[i - 1]:\n                    ps = i\n                    for j in range(i + 1, len(a)):\n                        if a[j] > a[i - 1] and a[ps] > a[j]:\n                            ps = j\n                    a[ps], a[i - 1] = a[i - 1], a[ps]\n                    p1 = i\n                    p2 = len(a) - 1\n                    while p1 < p2:\n                        a[p1], a[p2] = a[p2], a[p1]\n                        p1 += 1\n                        p2 -= 1\n                    return True\n            return False\n                    \n        n = 1\n        for i in range(1, len(tiles) + 1):\n            n *= i\n        a = set()\n        perm = []\n        for i in range(len(tiles)):\n            perm.append(i)\n        for _ in range(n):\n            cur = ''\n            for i in range(len(tiles)):\n                cur += tiles[perm[i]]\n            for i in range(len(tiles)):\n                a.add(cur[:i + 1])\n            next_permutation(perm)\n        return len(a)"
_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: 20559