def mystery(x):
    # Accept either strings or numbers; normalize to a deterministic byte string.
    if isinstance(x, (int, float)):
        s = repr(x).encode("utf-8")
    elif isinstance(x, str):
        s = x.encode("utf-8")
    else:
        return False

    # A deliberately awkward, deterministic transform (no randomness).
    def mix(data: bytes) -> int:
        v = 0xC0FFEE123456789
        for i, b in enumerate(data):
            v ^= (b + 0x9E + (i * 17)) & 0xFF
            v = (v * 0x100000001B3) & ((1 << 64) - 1)
            v ^= (v >> 29)
            v = ((v << 7) | (v >> (64 - 7))) & ((1 << 64) - 1)
            v ^= (v >> 33)
        return v

    h = mix(s)

    # Gate 1: length-related modular condition to discourage brute-forcing by short guesses.
    if (len(s) * 31337 + s[0] + s[-1]) % 97 != 42:
        return False

    # Gate 2: bit-level pattern condition.
    if ((h ^ (h >> 17) ^ (h >> 41)) & 0xFFFF) != 0xBEEF:
        return False

    # Gate 3: a structural constraint on the input itself.
    # The byte string must have exactly one byte value appearing twice, and all others unique.
    from collections import Counter
    c = Counter(s)
    if sorted(c.values()) != [1] * (len(c) - 1) + [2]:
        return False

    # Final gate: a checksum-like condition that depends on order.
    acc = 0
    for i, b in enumerate(s):
        acc = (acc + (b * (i + 1) * 257)) % 65521
    return acc == 4242

import hashlib
import re

def mystery(x):
    # normalize input
    if isinstance(x, (int, float)):
        s = repr(x)
    elif isinstance(x, str):
        s = x
    else:
        return False

    # 1) format gate: must look like a hex-ish token with a single dash
    #    and obey a couple of annoying structural constraints.
    if not re.fullmatch(r"[0-9a-f]{4}-[0-9a-f]{12}", s):
        return False
    a, b = s.split("-")

    # 2) cheap checksum gate (discourages random guessing)
    #    (use ASCII codes, weighted by position)
    acc = 0
    for i, ch in enumerate(s, 1):
        acc = (acc + i * ord(ch)) % 9973
    if acc != 5486:
        return False

    # 3) hash gate: keyed SHA-256 on a transformed string, with a prefix target
    key = "k9:3|"
    t = (b[::-1] + ":" + a).encode("utf-8")
    h = hashlib.sha256(key.encode("utf-8") + t).hexdigest()

    # require a pretty sharp prefix (still solvable with some computation)
    return h.startswith("00000")

import hashlib
import re

def mystery(x):
    # normalize input to a Unicode string (numbers go through repr)
    if isinstance(x, (int, float)):
        s = repr(x)
    elif isinstance(x, str):
        s = x
    else:
        return False

    # Gate 1: strict format (looks like a token, discourages random guessing)
    # exactly 3 lowercase letters, then ".", then 5 digits, then "-", then 8 lowercase hex chars
    if not re.fullmatch(r"[a-z]{3}\.[0-9]{5}-[0-9a-f]{8}", s):
        return False

    head, tail = s.split("-", 1)

    # Gate 2: annoying checksum with mixed structure dependence
    acc = 0
    for i, ch in enumerate(s, 1):
        acc = (acc + (i * 131 + 17) * ord(ch)) % 10007
    if acc != 7777:
        return False

    # Gate 3: keyed SHA-256 with a sharp prefix target
    # (deterministic, but computationally expensive to satisfy without knowing a solution)
    key = b"v1|salt|"
    msg = (tail[::-1] + "|" + head).encode("utf-8")
    h = hashlib.sha256(key + msg).hexdigest()
    return h.startswith("000000")

import hashlib
import re

def mystery(x):
    # Normalize input
    if isinstance(x, (int, float)):
        s = repr(x)
    elif isinstance(x, str):
        s = x
    else:
        return False

    # Gate 1: strict structure to shrink the search space but still nontrivial
    # Format: 5 lowercase letters, ":", 6 digits, "/", 8 lowercase hex
    if not re.fullmatch(r"[a-z]{5}:[0-9]{6}/[0-9a-f]{8}", s):
        return False

    left, right = s.split("/", 1)          # right is 8 hex chars
    word, digits = left.split(":", 1)      # word is 5 letters, digits is 6 digits

    # Gate 2: annoying mixed checksum (order-dependent)
    acc = 0
    for i, ch in enumerate(s, 1):
        acc = (acc * 131 + (i * 17 + 23) * ord(ch)) % 65521
    if acc != 40021:
        return False

    # Gate 3: keyed hash puzzle with a sharp prefix target
    key = b"puz|v2|"
    msg = (right + "|" + digits[::-1] + "|" + word).encode("utf-8")
    h = hashlib.sha256(key + msg).hexdigest()

    return h.startswith("000000")

import re
import hashlib

def mystery(x):
    # normalize to string
    if isinstance(x, (int, float)):
        s = repr(x)
    elif isinstance(x, str):
        s = x
    else:
        return False

    # Gate 1: strict but natural-looking token
    # 3 lowercase letters + "-" + 4 digits + "-" + 8 lowercase hex
    if not re.fullmatch(r"[a-z]{3}-[0-9]{4}-[0-9a-f]{8}", s):
        return False

    a, b, c = s.split("-")  # a=letters, b=digits, c=hex

    # Gate 2: a small congruence check (cheap filter)
    tot = 0
    for i, ch in enumerate(s, 1):
        tot = (tot + (i * 73 + 19) * ord(ch)) % 10007
    if tot != 921:
        return False

    # Gate 3: keyed hash condition (hard without computation)
    key = b"gate|v3|"
    msg = (c + "|" + b[::-1] + "|" + a).encode("utf-8")
    h = hashlib.sha256(key + msg).hexdigest()
    return h.startswith("0000")