


'''simple docstring'''
from __future__ import annotations

def 					lowerCamelCase_ ( __UpperCamelCase					:       list							,    __UpperCamelCase					:       int | None = None							,    __UpperCamelCase					:       int | None = None		)					->	None:







     """simple docstring"""
     if start is None:
          _A				=							0

     if end is None:
          _A				=							len(__UpperCamelCase		) - 1

     if start >= end:
          return

     _A				=							(start + end) // 2

     slowsort(__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase		)
     slowsort(__UpperCamelCase							,    mid + 1							,    __UpperCamelCase		)

     if sequence[end] < sequence[mid]:
          _A		,				_A				=							sequence[mid], sequence[end]

     slowsort(__UpperCamelCase							,    __UpperCamelCase							,    end - 1		)


if __name__ == "__main__":
    from doctest import testmod

    testmod()









'''simple docstring'''
def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	bool:







     """simple docstring"""
     return str(__UpperCamelCase		) == str(__UpperCamelCase		)[::-1]

def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	int:







     """simple docstring"""
     return int(__UpperCamelCase		) + int(str(__UpperCamelCase		)[::-1]		)

def 					lowerCamelCase_ ( __UpperCamelCase					:       int = 1_0_0_0_0		)					->	int:







     """simple docstring"""
     _A				=							[]
     for num in range(1							,    __UpperCamelCase		):
          _A				=							0
          _A				=							num
          while iterations < 5_0:
               _A				=							sum_reverse(__UpperCamelCase		)
               iterations += 1
               if is_palindrome(__UpperCamelCase		):
                    break
          else:
               lychrel_nums.append(__UpperCamelCase		)
     return len(__UpperCamelCase		)


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





