def mystery(x):
    """
    Returns True only for a very specific 5-digit number.
    """
    s = str(x)
    # Must be exactly 5 characters, all digits, and no leading zeros.
    if len(s) != 5 or not s.isdigit():
        return False
    n = int(s)
    if n < 10000:
        return False
    # The cube of the number must end with the same 5 digits.
    return (n ** 3) % 100000 == n

def mystery(x):
    """
    Returns True only for a very specific 12-character alphanumeric string.
    """
    if not isinstance(x, str):
        return False
    if len(x) != 12:
        return False
    if not x.isalnum():
        return False
    # Sum of character codes must be exactly 1000
    if sum(ord(c) for c in x) != 1000:
        return False
    # Product of character codes modulo 1000000007 must match
    prod = 1
    for c in x:
        prod = (prod * ord(c)) % 1000000007
    if prod != 379797897:
        return False
    # Polynomial rolling hash modulo 1000000009 must match
    h = 0
    for c in x:
        h = (h * 31 + ord(c)) % 1000000009
    if h != 525182534:
        return False
    return True

def mystery(x):
    """
    Returns True only for a very specific 5-digit integer.
    """
    if not isinstance(x, int):
        return False
    # Must be a 5-digit number
    if x < 10000 or x > 99999:
        return False
    s = str(x)
    # Sum of digits must be 17
    if sum(int(c) for c in s) != 17:
        return False
    # Product of digits must be 128
    prod = 1
    for c in s:
        prod *= int(c)
    if prod != 128:
        return False
    # Modular constraints
    if x % 3 != 2:
        return False
    if x % 5 != 3:
        return False
    if x % 7 != 4:
        return False
    if x % 11 != 5:
        return False
    if x % 13 != 6:
        return False
    # Square modulo constraint
    if (x * x) % 12345 != 2674:
        return False
    return True

def mystery(x):
    if not isinstance(x, str):
        return False
    if len(x) != 16:
        return False
    if not x.isalnum():
        return False
    # Sum of character codes must be exactly 1613
    if sum(ord(c) for c in x) != 1613:
        return False
    # Product of character codes modulo 1000000007 must equal 85542237
    prod = 1
    for c in x:
        prod = (prod * ord(c)) % 1000000007
    if prod != 85542237:
        return False
    # First polynomial rolling hash: base 31 modulo 1000000009
    h1 = 0
    for c in x:
        h1 = (h1 * 31 + ord(c)) % 1000000009
    if h1 != 284314030:
        return False
    # Second polynomial rolling hash: base 37 modulo 1000003
    h2 = 0
    for c in x:
        h2 = (h2 * 37 + ord(c)) % 1000003
    if h2 != 144381:
        return False
    return True

def mystery(x):
    """
    Returns True only for a very specific 12-character alphanumeric string.
    """
    if not isinstance(x, str):
        return False
    if len(x) != 12:
        return False
    if not x.isalnum():
        return False
    # Must contain at least one digit, one lowercase, one uppercase
    if not (any(c.isdigit() for c in x) and any(c.islower() for c in x) and any(c.isupper() for c in x)):
        return False
    # Sum of character codes
    if sum(ord(c) for c in x) != 986:
        return False
    # Product of character codes modulo 1000000007
    prod = 1
    for c in x:
        prod = (prod * ord(c)) % 1000000007
    if prod != 465263569:
        return False
    # Polynomial rolling hash with base 31 modulo 1000000009
    h1 = 0
    for c in x:
        h1 = (h1 * 31 + ord(c)) % 1000000009
    if h1 != 837848973:
        return False
    # Polynomial rolling hash with base 37 modulo 999983
    h2 = 0
    for c in x:
        h2 = (h2 * 37 + ord(c)) % 999983
    if h2 != 817040:
        return False
    # Base-36 numeric value modulo 1000000007
    try:
        val = int(x.lower(), 36)
    except ValueError:
        return False
    if val % 1000000007 != 738415655:
        return False
    return True