def mystery(x):
    s = str(x).lower()
    if not (len(s) == 8 and s.isalpha() and s.islower()):
        return False

    p = (5, 3, 7, 1, 6, 0, 4, 2)
    shifts = (11, 4, 15, 1, 12, 6, 18, 3)

    t = ''.join(
        chr((ord(s[::-1][p[i]]) - 97 + shifts[i]) % 26 + 97)
        for i in range(8)
    )

    goal = ''.join(
        chr(((n * 7) + 3) % 26 + 97)
        for n in (9, 5, 22, 23, 21, 18, 4, 12)
    )

    return t == goal

def mystery(x):
    s = str(x).lower()
    if len(s) != 8 or any(c < "a" or c > "z" for c in s):
        return False

    M = 26 ** 4

    def pack(n):
        return "".join(chr(97 + (n // (26 ** i)) % 26) for i in range(4))

    a = sum((ord(s[i]) - 97) * (26 ** (i // 2)) for i in range(0, 8, 2))
    b = sum((ord(s[i]) - 97) * (26 ** (i // 2)) for i in range(1, 8, 2))

    for _ in range(2):
        a, b = ((17 * a + 5 * b + 12345) % M,
                (4 * a + 11 * b + 54321) % M)

    return pack(a) == "yvrw" and pack(b) == "ectt"

def mystery(x):
    s = str(x).lower()
    if not (len(s) == 12 and s.isalpha() and s.islower()):
        return False

    if sum((i + 1) * (ord(c) - 96) for i, c in enumerate(s)) % 11 != 1:
        return False

    u = s[4:8] + s[8:12] + s[:4]
    M = 26 ** 4

    def val(t):
        n = 0
        for ch in t:
            n = n * 26 + (ord(ch) - 97)
        return n

    def pack(n):
        return ''.join(chr(97 + (n // p) % 26) for p in (26**3, 26**2, 26, 1))

    a, b, c = map(val, (u[:4], u[4:8], u[8:12]))

    for _ in range(2):
        a, b, c = (
            (9 * a + 2 * b + 5 * c + 12345) % M,
            (7 * b + 4 * c + 23456) % M,
            (5 * c + 34567) % M,
        )

    return pack(a) == "oimm" and pack(b) == "qmba" and pack(c) == "luva"

def mystery(x):
    s = str(x).lower()
    if not (len(s) == 12 and s.isascii() and s.isalpha() and s.islower()):
        return False

    if sum((i + 1) * (ord(c) - 96) for i, c in enumerate(s)) % 17 != 10:
        return False
    if sum(ord(c) for c in s) % 13 != 7:
        return False

    t = (
        s[8] + s[1] + s[10] + s[3] +
        s[6] + s[11] + s[0] + s[5] +
        s[2] + s[9] + s[4] + s[7]
    )

    M = 26 ** 3

    def pack(chunk):
        n = 0
        for ch in chunk:
            n = n * 26 + (ord(ch) - 97)
        return n

    a, b, c, d = map(pack, (t[:3], t[3:6], t[6:9], t[9:12]))

    for k in (5, 17, 9, 14, 23):
        a, b, c, d = (
            (3 * a + 5 * b + 7 * c + 11 * d + k) % M,
            a,
            b,
            c,
        )

    return (a, b, c, d) == (2749, 599, 130, 32)

def mystery(x):
    A = "0123456789abcdefghijklmnopqrstuvwxyz"
    idx = {c: i for i, c in enumerate(A)}

    s = str(x).lower()
    if len(s) != 14 or any(c not in idx for c in s):
        return False

    v = [idx[c] for c in s]

    if sum(v) % 19 != 7:
        return False
    if sum((i + 1) * v[i] for i in range(14)) % 23 != 11:
        return False
    if (v[0] + 2 * v[6] + 3 * v[13]) % 17 != 3:
        return False

    u = v[5:] + v[:5]
    u = [(u[i] + 7 * i + 3) % 36 for i in range(14)]
    w = [(u[i] + 2 * u[(i + 1) % 14] + u[(i + 7) % 14]) % 36 for i in range(14)]

    goal = (3, 31, 26, 19, 7, 35, 27, 29, 27, 24, 9, 33, 25, 1)
    return tuple(w) == goal