def mystery(x):
    import hashlib, hmac

    # Accept either a string or a (Python) integer.
    if isinstance(x, str):
        b = x.encode("utf-8", "strict")
    elif isinstance(x, int):
        b = str(x).encode("ascii", "strict")
    else:
        return False

    # Quick reject: exact byte length required.
    if len(b) != 16:
        return False

    def _ror8(v, r):
        r &= 7
        return v if r == 0 else (((v >> r) | (v << (8 - r))) & 0xFF)

    # Reconstruct the hidden 16-byte secret (as bytes) via a reversible per-byte transform.
    enc = (
        0x7E, 0xC5, 0xD8, 0x43,
        0xE8, 0x5C, 0x57, 0x0B,
        0xF4, 0x20, 0x10, 0x7F,
        0x28, 0x0E, 0x47, 0x5E
    )

    secret = bytearray(16)
    for i, t in enumerate(enc):
        r = (i * 3 + 1) & 7
        a = (i * 17 + 23) & 0xFF
        xmask = (0xA5 ^ ((i * 11) & 0xFF)) & 0xFF
        v = t ^ xmask
        v = (v - a) & 0xFF
        v = _ror8(v, r)
        secret[i] = v
    secret = bytes(secret)

    # Derive a per-input key (so you can't just precompute one fixed digest target).
    salt = bytes((((i * 73 + 41) ^ (i >> 1) ^ 0xA6) & 0xFF) for i in range(32))
    key = hashlib.sha256(salt + b"mystery" + b[::-1]).digest()[:16]

    # Compare keyed hashes (constant-time).
    got = hashlib.blake2s(b, key=key, digest_size=32).digest()
    want = hashlib.blake2s(secret, key=key, digest_size=32).digest()
    return hmac.compare_digest(got, want)

def mystery(x):
    import hashlib, hmac

    # Accept either a string or a (Python) integer.
    if isinstance(x, str):
        b = x.encode("utf-8", "strict")
    elif isinstance(x, int):
        # Integers are converted via their base-10 textual form.
        b = str(x).encode("ascii", "strict")
    else:
        return False

    # Fixed-length gate.
    if len(b) != 24:
        return False

    def _ror8(v, r):
        r &= 7
        return ((v >> r) | ((v << (8 - r)) & 0xFF)) & 0xFF

    # Reconstruct a hidden 24-byte secret via a reversible stream-ish transform.
    enc = (
        65, 120, 115, 54, 145, 113, 18, 62,
        173, 192, 83, 75, 116, 125, 10, 199,
        65, 136, 181, 95, 74, 54, 240, 222
    )

    s = 0xC3
    prev = 0x5A
    secret = bytearray()
    for i, e in enumerate(enc):
        s = (s * 5 + 17 + i) & 0xFF
        w = e ^ prev
        u = (w - (13 * i)) & 0xFF
        r = (i % 7) + 1
        t = _ror8(u, r)  # inverse of the encoder's rotate-left
        secret.append(t ^ s)
        prev = e
    secret = bytes(secret)

    # Per-input key schedule (depends on the candidate itself).
    salt = hashlib.sha256(b"::".join([
        bytes(enc),
        bytes(((i * 29 + 7) ^ (enc[i % 24] + i)) & 0xFF for i in range(64)),
        secret[:8][::-1],
    ])).digest()

    iters = 20000 + (sum(b) & 1023)
    key = hashlib.pbkdf2_hmac("sha256", b[::-1] + bytes([len(b)]), salt, iters, dklen=32)

    # If b == secret then these match; otherwise you need to solve a nasty fixed-point-ish condition.
    got = hmac.new(key, b, hashlib.sha3_256).digest()
    want = hmac.new(key, secret, hashlib.sha3_256).digest()
    return hmac.compare_digest(got, want)

def mystery(x):
    import hashlib, hmac

    # Normalize input to bytes.
    if isinstance(x, str):
        b = x.encode("utf-8", "strict")
    elif isinstance(x, int):
        b = str(x).encode("ascii", "strict")
    else:
        return False

    # Fixed-length gate.
    if len(b) != 28:
        return False

    def _ror8(v, r):
        r &= 7
        return ((v >> r) | ((v << (8 - r)) & 0xFF)) & 0xFF

    # Hidden target, stored as a chained/rotated encoding.
    enc = bytes((
        163, 176, 37, 38, 220, 189, 1, 224, 171, 204, 71, 68, 148, 164,
        147, 25, 199, 30, 230, 17, 99, 81, 178, 17, 90, 240, 174, 98
    ))

    # Decode to reconstruct the secret (28 bytes).
    s = 0xC7
    prev = 0x3A
    out = bytearray()
    for i, e in enumerate(enc):
        s = (s * 11 + 19 + i) & 0xFF
        u = e ^ prev
        r = (i % 7) + 1
        tplus = _ror8(u, r)
        t = (tplus - (5 * i)) & 0xFF
        out.append(t ^ s)
        prev = e
    secret = bytes(out)

    # Per-input expensive key schedule (depends on b, but salt depends on the hidden secret).
    salt = hashlib.sha256(enc + b"|m|" + secret[::3] + bytes([enc[0] ^ enc[-1]])).digest()
    iters = 35000 + ((enc[0] ^ enc[-1] ^ sum(b)) & 4095)
    key = hashlib.pbkdf2_hmac("sha256", b[::-1] + bytes([len(b)]), salt, iters, dklen=32)

    # If b == secret, HMACs match; otherwise you’re up against an (effectively) collision search.
    got = hmac.new(key, b, hashlib.sha3_256).digest()
    want = hmac.new(key, secret, hashlib.sha3_256).digest()
    return hmac.compare_digest(got, want)

def mystery(x):
    import hashlib, hmac, unicodedata

    # Normalize input to bytes (strings go through Unicode normalization first).
    if isinstance(x, str):
        x = unicodedata.normalize("NFKC", x)
        b = x.encode("utf-8", "strict")
    elif isinstance(x, int):
        b = str(x).encode("ascii", "strict")
    else:
        return False

    # Fixed-length gate (in bytes).
    if len(b) != 31:
        return False

    def _ror8(v, r):
        r &= 7
        return ((v >> r) | ((v << (8 - r)) & 0xFF)) & 0xFF

    # Encoded 31-byte target (reversible).
    enc = bytes((
        147, 34, 204, 163, 74, 7, 90, 33, 13, 236,
        158, 71, 79, 219, 81, 106, 133, 169, 22, 145,
        90, 75, 111, 163, 147, 209, 148, 68, 118, 206,
        203
    ))

    # Decode to reconstruct the hidden 31-byte secret.
    secret = bytearray(31)
    for i, e in enumerate(enc):
        r = (i * 5 + 1) & 7
        mask = (i * 17 + 93) & 0xFF
        t = e ^ mask
        secret[i] = _ror8(t, r)
    secret = bytes(secret)

    # Expensive per-input key schedule (depends on candidate and on the hidden secret).
    salt = hashlib.sha256(
        enc +
        b"|m|" +
        bytes([len(b), enc[0] ^ enc[-1]]) +
        secret[::2] +
        secret[::-3]
    ).digest()

    iters = 22000 + ((sum(b) + (b[0] ^ b[-1]) + enc[7]) & 4095)
    key = hashlib.pbkdf2_hmac(
        "sha512",
        b + b[::-1] + bytes([b[0] ^ 0xA7, b[-1] ^ 0x3C]),
        salt,
        iters,
        dklen=32,
    )

    # Constant-time keyed hash comparison.
    got = hashlib.blake2s(b, key=key[:16], digest_size=32).digest()
    want = hashlib.blake2s(secret, key=key[:16], digest_size=32).digest()
    return hmac.compare_digest(got, want)

def mystery(x):
    import hashlib, hmac, unicodedata

    # --- normalize input to bytes ---
    if isinstance(x, str):
        x = unicodedata.normalize("NFKC", x)
        b = x.encode("utf-8", "strict")
    elif isinstance(x, int):
        # Integers are converted via their base-10 textual form.
        b = str(x).encode("ascii", "strict")
    else:
        return False

    # Fixed-size gate (bytes, not characters).
    if len(b) != 33:
        return False

    def _ror8(v, r):
        r &= 7
        return v if r == 0 else (((v >> r) | (v << (8 - r))) & 0xFF)

    # --- reconstruct a hidden 33-byte target (secret) ---
    enc = bytes((
        10, 223, 31, 67, 213, 185, 173, 193, 63, 15, 82,
        122, 172, 147, 166, 15, 236, 10, 48, 25, 31,
        122, 188, 150, 182, 212, 248, 223, 78, 78, 26,
        33, 209
    ))

    secret = bytearray(33)
    for i, e in enumerate(enc):
        a = (11 * i + 3) & 0xFF
        r = (3 * i + 1) & 7
        m = (0xA5 ^ ((17 * i + 93) & 0xFF)) & 0xFF

        u = e ^ m
        t0 = _ror8(u, r)
        secret[i] = (t0 - a) & 0xFF
    secret = bytes(secret)

    # --- per-input expensive key schedule (depends on code object too) ---
    code_f = hashlib.sha256(
        mystery.__code__.co_code +
        bytes([mystery.__code__.co_argcount, mystery.__code__.co_nlocals & 0xFF]) +
        b"::mystery::"
    ).digest()

    salt = hashlib.sha256(
        code_f +
        enc +
        secret[::2] +
        bytes([enc[0] ^ enc[-1]])
    ).digest()

    iters = 26000 + ((code_f[0] ^ b[0] ^ b[-1] ^ sum(b)) & 4095)
    key = hashlib.pbkdf2_hmac(
        "sha512",
        b + code_f[:9] + b[::-1] + bytes([len(b) ^ code_f[-1]]),
        salt,
        iters,
        dklen=32
    )

    # Constant-time keyed hash comparison.
    got = hashlib.blake2s(b, key=key[:16], digest_size=32).digest()
    want = hashlib.blake2s(secret, key=key[:16], digest_size=32).digest()
    return hmac.compare_digest(got, want)