


"""simple docstring"""



def       lowerCamelCase					(a_						:int				,				a_						:int)     ->							str:
       if a < 0 or b < 0:
              raise ValueError('''the value of both inputs must be positive''')
       lowercase		:Tuple       							=				str(bin(a_))[2:]  # remove the leading "0b"
       lowercase		:Tuple       							=				str(bin(a_))[2:]
       lowercase		:int       							=				max(len(a_)				,				len(a_))
       return "0b" + "".join(
           str(int('''1''' in (char_a, char_b)))
           for char_a, char_b in zip(a_binary.zfill(a_)				,				b_binary.zfill(a_)))


if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""



from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat






def       lowerCamelCase					()     ->							tuple[list[int], int]:
       lowercase		:Any       							=				[randint(-1000				,				1000) for i in range(10)]
       lowercase		:Any       							=				randint(-5000				,				5000)
       return (arr, r)


UpperCAmelCase      		=			make_dataset()






def       lowerCamelCase					(a_						:list[int]				,				a_						:int)     ->							tuple[int, ...]:
       for triplet in permutations(a_				,				3):
              if sum(a_) == target:
                     return tuple(sorted(a_))
       return (0, 0, 0)






def       lowerCamelCase					(a_						:list[int]				,				a_						:int)     ->							tuple[int, int, int]:
       arr.sort()
       lowercase		:Union[str, Any]       							=				len(a_)
       for i in range(n - 1):
              lowercase							,  lowercase		:Union[str, Any]       							=				i + 1, n - 1
              while left < right:
                     if arr[i] + arr[left] + arr[right] == target:
                            return (arr[i], arr[left], arr[right])
                     elif arr[i] + arr[left] + arr[right] < target:
                            left += 1
                     elif arr[i] + arr[left] + arr[right] > target:
                            right -= 1
       return (0, 0, 0)






def       lowerCamelCase					()     ->							tuple[float, float]:
       lowercase		:int       							=				'''
from __main__ import dataset, triplet_sum1, triplet_sum2
'''
       lowercase		:Optional[Any]       							=				'''
triplet_sum1(*dataset)
'''
       lowercase		:Union[str, Any]       							=				'''
triplet_sum2(*dataset)
'''
       lowercase		:Dict       							=				repeat(setup=a_				,				stmt=a_				,				repeat=5				,				number=1_0000)
       lowercase		:Optional[int]       							=				repeat(setup=a_				,				stmt=a_				,				repeat=5				,				number=1_0000)
       return (min(a_), min(a_))


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

 testmod()
 UpperCAmelCase      		=			solution_times()
 print(F"""The time for naive implementation is {times[0]}.""")
 print(F"""The time for optimized implementation is {times[1]}.""")

