magnitude = lambda bits: 1_000_000_000_000_000_000 % (2 ** bits)
sign = lambda bits: -1 ** (1_000_000_000_000_000_000 // (2 ** bits))

print("64 bit sum:", magnitude(64) * sign(64))
print("32 bit sum:", magnitude(32) * sign(32))
print("16 bit sum:", magnitude(16) * sign(16))

#question1.py
def rose(n) :
  if n==0 : 
    yield []
  else :
    for k in range(0,n) :    
      for l in rose(k) :
        for r in rose(n-1-k) :      
            yield [l]+[r]+[r]
            
def start(n) :
  for x in rose(n) : 
      print(x) #basically I am printing x for each rose(n) file


print("starting program: \n")
start(2) # here is where I call the start function

x[cat_var].isnull().sum().sort_values(ascending=False)

import math

def factorial(n):
    print(math.factorial(n))
    return (math.factorial(n))
    
factorial(5)
factorial(10)
factorial(15)

def sum_of_powers(end, power = 2, start = 1):
  return sum([(i) ** power for i in range(start, end + 1)])

sum_of_powers(10) # 385
sum_of_powers(10, 3) # 3025
sum_of_powers(10, 3, 5) # 2925

#You are given a two-digit integer n. Return the sum of its digits.
#Example
#For n = 29 the output should be solution (n) = 11
def solution(n):
    return (n//10 + n%10)