def mystery(x):
n = 1000000016000000063
return isinstance(x, int) and x > 1 and x != n and n % x == 0
def mystery(x):
if not isinstance(x, int): return False
if x < 0 or x >= 2**32: return False
# Bit-reverse x within 32 bits
y = 0
n = x
for _ in range(32):
y = (y << 1) | (n & 1)
n >>= 1
return (x ^ y) == 0xA5A5A5A5 and bin(x).count('1') == 16
def mystery(x):
n = 1000000007037000000259
return isinstance(x, int) and x > 10**9 and x != n and n % x == 0
def mystery(x):
if not isinstance(x, int): return False
if x < 10**9 or x >= 10**10: return False
s = str(x)
if len(set(s)) != 10: return False
ds = [int(c) for c in s]
P = [17, 13, 11, 7, 5, 3, 2]
for i in range(7):
n = ds[7-i] * 100 + ds[8-i] * 10 + ds[9-i]
if n % P[i] != 0:
return False
return True
def mystery(x):
n = 1000000000000128000003367
return isinstance(x, int) and x > 10**12 and x != n and n % x == 0
def mystery(x):
if not isinstance(x, int): return False
if x < 0 or x >= 2**60: return False
# Count set bits
if bin(x).count('1') != 30: return False
# Specific bit patterns at the ends
if (x & 0xF) != 0xA: return False
if ((x >> 56) & 0xF) != 0x5: return False
# Sum of set bit positions
s = 0
for i in range(60):
if (x >> i) & 1:
s += i
return s == 900
def mystery(x):
n = 100000000023600000007363
return isinstance(x, int) and x > 10**12 and x != n and n % x == 0
def mystery(x):
if not isinstance(x, int): return False
if x < 0 or x >= 2**100: return False
bits = [(x >> i) & 1 for i in range(100)]
if sum(bits) != 50: return False
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
for p in primes:
if bits[p] != 1: return False
s1 = sum(i for i, b in enumerate(bits) if b == 1)
s2 = sum(i*i for i, b in enumerate(bits) if b == 1)
return s1 == 2500 and s2 == 151372
def mystery(x):
if not isinstance(x, int): return False
if x < 0 or x >= 2**64: return False
bits = [(x >> i) & 1 for i in range(64)]
if sum(bits) != 32: return False
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61]
for p in primes:
if bits[p] != 1: return False
s1 = sum(i for i, b in enumerate(bits) if b)
s2 = sum(i*i for i, b in enumerate(bits) if b)
xor_val = 0
for i, b in enumerate(bits):
if b: xor_val ^= i
return s1 == 655 and s2 == 22761 and xor_val == 57
def mystery(x):
if not isinstance(x, int): return False
if x < 0 or x >= 2**80: return False
bits = [(x >> i) & 1 for i in range(80)]
if sum(bits) != 40: return False
s = sum(i for i, b in enumerate(bits) if b)
s2 = sum(i*i for i, b in enumerate(bits) if b)
s3 = sum(i*i*i for i, b in enumerate(bits) if b)
xor_val = 0
for i, b in enumerate(bits):
if b: xor_val ^= i
return s == 1580 and s2 == 67740 and s3 == 3096800 and xor_val == 0