





'''simple docstring'''

from __future__ import annotations







def  a__    (    lowercase :					list[int | float], lowercase :					int, lowercase :					int				)		->		int | float:





     """simple docstring"""

     if len(lowercase				) == 0:
          raise ValueError('''find_max() arg is an empty sequence'''				)
     if (
         left >= len(lowercase				)
         or left < -len(lowercase				)
         or right >= len(lowercase				)
         or right < -len(lowercase				)
     ):
          raise IndexError('''list index out of range'''				)
     if left == right:
          return nums[left]
     _UpperCamelCase       =	(left + right) >> 1  # the middle
     _UpperCamelCase       =	find_max(lowercase, lowercase, lowercase				)  # find max in range[left, mid]
     _UpperCamelCase       =	find_max(lowercase, mid + 1, lowercase				)  # find max in range[mid + 1, right]

     return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)










'''simple docstring'''

def  a__    (    lowercase :					int, lowercase :					int				)		->		int:





     """simple docstring"""

     return x if y == 0 else greatest_common_divisor(lowercase, x % y				)







def  a__    (    lowercase :					int, lowercase :					int				)		->		int:





     """simple docstring"""

     return (x * y) // greatest_common_divisor(lowercase, lowercase				)







def  a__    (    lowercase :					int = 20				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	1
     for i in range(1, n + 1				):
          _UpperCamelCase       =	lcm(lowercase, lowercase				)
     return g


if __name__ == "__main__":
   print(F"""{solution() = }""")



