A *Vampire number* is a positive integer `z` with a factorization `x * y = z` such that

- `x` and `y` have the same number of digits and
- the multiset of digits of `z` is equal to the multiset of digits of `x` and `y`.
- Additionally, to avoid trivialities, `x` and `y` may not both end with `0`.

In this case, `x` and `y` are called *fangs* of `z`. (The fangs of a Vampire number may not be unique, but this shouldn't bother us.) The first three Vampire numbers are

```
1260 = 21*60
1395 = 15*93
1435 = 35*41
```

Write an algorithm that on input `k` returns the `k`th Vampire number. To avoid time-outs, the Python version will test with `1 <= k <= 155`.

PS: In the OEIS, the Vampire numbers are sequence [A014575](https://oeis.org/A014575).

PPS: So called *Pseudo-Vampire Numbers* are treated in [this kata](http://www.codewars.com/kata/vampire-numbers-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 = "from itertools import combinations\n\nvampires = set()\nfor i in [1, 2]:\n    for x, y in combinations(range(10**i, 10**(i+1)), 2):\n        if x % 10 == 0 == y % 10:\n            continue\n        z = x * y\n        if sorted(str(z)) == sorted(f'{x}{y}'):\n            vampires.add(z)\nxs = sorted(vampires)\n\ndef VampireNumber(i):\n    return xs[i-1]"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'VampireNumber'
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: 5294