def mystery(x):
    # Input must be an 8-character string
    if not isinstance(x, str) or len(x) != 8:
        return False
    
    # Convert characters to ASCII integers
    v = [ord(c) for c in x]
    
    # Constraint 1: The sum of the ASCII values must be exactly 695
    if sum(v) != 695:
        return False
    
    # Constraint 2: A cyclic XOR transformation must match the target
    # The transformation is: next_val = ((current_char XOR next_char) + 42) % 256
    # Note: The last character is XORed with the first character (cyclic)
    
    target = [101, 86, 58, 107, 124, 52, 116, 126]
    
    transformed = []
    for i in range(8):
        # XOR current character with the next one (wrapping around at the end)
        xor_val = v[i] ^ v[(i + 1) % 8]
        # Add a constant offset and keep it within byte range
        val = (xor_val + 42) & 0xFF
        transformed.append(val)
        
    return transformed == target

def mystery(x):
    # Input must be a 6-character string
    if not isinstance(x, str) or len(x) != 6:
        return False
    
    v = [ord(c) for c in x]
    
    # Constraint 1: Cyclic Transformation
    # The sum of adjacent characters (wrapping around) XORed with the index
    # must match the target list.
    target = [189, 202, 203, 199, 160, 158]
    
    transformed = []
    for i in range(6):
        # Calculate (Current Char + Next Char) XOR Index
        val = (v[i] + v[(i + 1) % 6]) ^ i
        transformed.append(val)
        
    if transformed != target:
        return False
        
    # Constraint 2: Non-linear Modular Arithmetic
    # A specific combination of characters must satisfy this modulo equation.
    if (v[0] * v[2] + v[4]) % 1337 != 1030:
        return False
        
    return True

def mystery(x):
    # Input must be a 9-character string
    if not isinstance(x, str) or len(x) != 9:
        return False
    
    v = [ord(c) for c in x]
    
    # Imagine the 9 characters as a 3x3 grid:
    # 0 1 2
    # 3 4 5
    # 6 7 8
    
    # Constraint 1: Row Sums (Arithmetic)
    # The sum of ASCII values in each row must match these targets.
    if sum(v[0:3]) != 291: return False
    if sum(v[3:6]) != 291: return False
    if sum(v[6:9]) != 187: return False
    
    # Constraint 2: Column XOR Sums
    # The XOR sum of each column must match these targets.
    if (v[0] ^ v[3] ^ v[6]) != 94: return False
    if (v[1] ^ v[4] ^ v[7]) != 30: return False
    if (v[2] ^ v[5] ^ v[8]) != 63: return False
    
    # Constraint 3: Main Diagonal Product (Modulo 257)
    # The product of the main diagonal (indices 0, 4, 8) modulo 257.
    if (v[0] * v[4] * v[8]) % 257 != 103: return False
    
    # Constraint 4: Anti-Diagonal Sum
    # The sum of the anti-diagonal (indices 2, 4, 6).
    if (v[2] + v[4] + v[6]) != 321: return False
    
    # Constraint 5: Local relationship
    # The absolute difference between top-middle (1) and middle-left (3).
    if abs(v[1] - v[3]) != 7: return False
    
    return True

def mystery(x):
    # Input must be an 8-character string
    if not isinstance(x, str) or len(x) != 8:
        return False
    
    v = [ord(c) for c in x]
    
    # Constraint 0: Range check
    # All characters must be standard printable ASCII (32-126)
    if any(c < 32 or c > 126 for c in v):
        return False
    
    # Constraint 1: Pairwise Sums
    # The sum of disjoint pairs (v[0]+v[1], v[2]+v[3], etc.) must match targets.
    sum_targets = [163, 226, 201, 96]
    current_sums = [v[2*i] + v[2*i+1] for i in range(4)]
    if current_sums != sum_targets:
        return False
        
    # Constraint 2: Linking XORs
    # The XOR of linking pairs (v[1]^v[2], v[3]^v[4], etc.) wrapping around
    # must match targets.
    # Pairs are: (1,2), (3,4), (5,6), (7,0)
    xor_targets = [92, 19, 69, 76]
    current_xors = [(v[2*i+1] ^ v[(2*i+2)%8]) for i in range(4)]
    if current_xors != xor_targets:
        return False
        
    # Constraint 3: Modular Checksum
    # The sum of squares of all values modulo 1009 must equal 791.
    if sum(val**2 for val in v) % 1009 != 791:
        return False
        
    return True

def mystery(x):
    # Input must be a 10-character string
    if not isinstance(x, str) or len(x) != 10:
        return False
    
    v = [ord(c) for c in x]
    
    # Constraint 1: Exact Sum
    # The sum of all ASCII values must be 999
    if sum(v) != 999:
        return False
    
    # Constraint 2: Cyclic XOR Chain
    # Each character XORed with the next one (wrapping around) must match the target
    target = [44, 11, 1, 40, 44, 18, 7, 17, 23, 49]
    xor_chain = [(v[i] ^ v[(i+1)%10]) for i in range(10)]
    if xor_chain != target:
        return False
        
    # Constraint 3: Weighted Sum Checksum
    # The sum of each character multiplied by its 1-based index, modulo 1000
    weighted_sum = sum(v[i] * (i+1) for i in range(10))
    if weighted_sum % 1000 != 742:
        return False
        
    # Constraint 4: Bitwise Shift Relationship
    # A specific relationship between the first character and the sixth character
    # v[0] left shifted by 2, XORed with v[5] right shifted by 2
    if ((v[0] << 2) ^ (v[5] >> 2)) != 276:
        return False
        
    return True