




def 	lowerCAmelCase_	(     lowerCamelCase:				Any   , lowerCamelCase:				Union[str, Any]  )    ->	Optional[int]:


      '''simple docstring'''




      if len(str(lowerCamelCase  )  ) == 1 or len(str(lowerCamelCase  )  ) == 1:
            return a * b

      lowerCamelCase__					     = max(len(str(lowerCamelCase  )  )   , len(str(lowerCamelCase  )  )  )
      lowerCamelCase__					     = ma // 2

      lowerCamelCase__     ,						lowerCamelCase__					     = divmod(lowerCamelCase   , 10**ma  )
      lowerCamelCase__     ,						lowerCamelCase__					     = divmod(lowerCamelCase   , 10**ma  )

      lowerCamelCase__					     = karatsuba(lowerCamelCase   , lowerCamelCase  )
      lowerCamelCase__					     = karatsuba((aa + aa)   , (ba + ba)  )
      lowerCamelCase__					     = karatsuba(lowerCamelCase   , lowerCamelCase  )

      return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)

def 	lowerCAmelCase_	(     )    ->	List[Any]:


      '''simple docstring'''




      print(karatsuba(1_54_63   , 2_34_89  )  )


if __name__ == "__main__":
      main()






import sys

sys.set_int_max_str_digits(0)  # type: ignore






def 			lowerCamelCase__	(__lowerCamelCase		):
     _SCREAMING_SNAKE_CASE				:		int  			=							[0] * 11
     _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							[0] * 11

     # mark last 9 numbers
     for _ in range(9		):
          _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							1
          _SCREAMING_SNAKE_CASE				:		str  			=							number // 10
     # flag
     _SCREAMING_SNAKE_CASE				:		int  			=							True

     # check last 9 numbers for pandigitality

     for x in range(9		):
          if not check_last[x + 1]:
               _SCREAMING_SNAKE_CASE				:		Any  			=							False
     if not f:
          return f

     # mark first 9 numbers
     _SCREAMING_SNAKE_CASE				:		str  			=							int(str(__lowerCamelCase		)[:9]		)

     for _ in range(9		):
          _SCREAMING_SNAKE_CASE				:		str  			=							1
          _SCREAMING_SNAKE_CASE				:		List[Any]  			=							number // 10

     # check first 9 numbers for pandigitality

     for x in range(9		):
          if not check_front[x + 1]:
               _SCREAMING_SNAKE_CASE				:		Any  			=							False
     return f






def 			lowerCamelCase__	(__lowerCamelCase		):
     _SCREAMING_SNAKE_CASE				:		List[str]  			=							[0] * 11

     # mark last 9 numbers
     for _ in range(9		):
          _SCREAMING_SNAKE_CASE				:		Dict  			=							1
          _SCREAMING_SNAKE_CASE				:		List[str]  			=							number // 10
     # flag
     _SCREAMING_SNAKE_CASE				:		List[Any]  			=							True

     # check last 9 numbers for pandigitality

     for x in range(9		):
          if not check_last[x + 1]:
               _SCREAMING_SNAKE_CASE				:		str  			=							False
     return f






def 			lowerCamelCase__	():
     _SCREAMING_SNAKE_CASE				:		Dict  			=							1
     _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							1
     _SCREAMING_SNAKE_CASE				:		List[str]  			=							2
     # temporary Fibonacci numbers

     _SCREAMING_SNAKE_CASE				:		Any  			=							1
     _SCREAMING_SNAKE_CASE				:		List[str]  			=							1
     _SCREAMING_SNAKE_CASE				:		str  			=							2
     # temporary Fibonacci numbers mod 1e9

     # mod m=1e9, done for fast optimisation
     _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							[0] * 1000000
     _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							1000000000

     for x in range(1000000		):
          _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							(aa + ba) % m
          _SCREAMING_SNAKE_CASE				:		int  			=							ba % m
          _SCREAMING_SNAKE_CASE				:		List[str]  			=							ca % m
          if checka(__lowerCamelCase		):
               _SCREAMING_SNAKE_CASE				:		List[Any]  			=							1

     for x in range(1000000		):
          _SCREAMING_SNAKE_CASE				:		Any  			=							a + b
          _SCREAMING_SNAKE_CASE				:		Dict  			=							b
          _SCREAMING_SNAKE_CASE				:		int  			=							c
          # perform check only if in tocheck
          if tocheck[x + 3] and check(__lowerCamelCase		):
               return x + 3  # first 2 already done
     return -1


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