





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> Any:




    """simple docstring"""




    _A     =							0
    _A     =							len(_SCREAMING_SNAKE_CASE				)

    for i in range(n - 1				):
        for j in range(i + 1							,     _SCREAMING_SNAKE_CASE				):
            if arr[i] > arr[j]:
                num_inversions += 1

    return num_inversions





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> Any:




    """simple docstring"""




    if len(_SCREAMING_SNAKE_CASE				) <= 1:
        return arr, 0
    _A     =							len(_SCREAMING_SNAKE_CASE				) // 2
    _A     =							arr[0:mid]
    _A     =							arr[mid:]

    _A,			_A     =							count_inversions_recursive(_SCREAMING_SNAKE_CASE				)
    _A,			_A     =							count_inversions_recursive(_SCREAMING_SNAKE_CASE				)
    _A,			_A     =							_count_cross_inversions(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)

    _A     =							inversion_p + inversions_q + cross_inversions
    return c, num_inversions





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> Optional[int]:




    """simple docstring"""




    _A     =							[]
    _A     =							_A     =							_A     =							0
    while i < len(_SCREAMING_SNAKE_CASE				) and j < len(_SCREAMING_SNAKE_CASE				):
        if p[i] > q[j]:
            # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
            # These are all inversions. The claim emerges from the
            # property that P is sorted.
            num_inversion += len(_SCREAMING_SNAKE_CASE				) - i
            r.append(q[j]				)
            j += 1
        else:
            r.append(p[i]				)
            i += 1

    if i < len(_SCREAMING_SNAKE_CASE				):
        r.extend(p[i:]				)
    else:
        r.extend(q[j:]				)

    return r, num_inversion





def 				__lowerCAmelCase(       )							-> Dict:




    """simple docstring"""




    _A     =							[10, 2, 1, 5, 5, 2, 11]

    # this arr has 8 inversions:
    # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

    _A     =							count_inversions_bf(_SCREAMING_SNAKE_CASE				)
    _A,			_A     =							count_inversions_recursive(_SCREAMING_SNAKE_CASE				)

    assert num_inversions_bf == num_inversions_recursive == 8

    print('number of inversions = '							,     _SCREAMING_SNAKE_CASE				)

    # testing an array with zero inversion (a sorted arr_1)

    arr_a.sort()
    _A     =							count_inversions_bf(_SCREAMING_SNAKE_CASE				)
    _A,			_A     =							count_inversions_recursive(_SCREAMING_SNAKE_CASE				)

    assert num_inversions_bf == num_inversions_recursive == 0
    print('number of inversions = '							,     _SCREAMING_SNAKE_CASE				)

    # an empty list should also have zero inversions
    _A     =							[]
    _A     =							count_inversions_bf(_SCREAMING_SNAKE_CASE				)
    _A,			_A     =							count_inversions_recursive(_SCREAMING_SNAKE_CASE				)

    assert num_inversions_bf == num_inversions_recursive == 0
    print('number of inversions = '							,     _SCREAMING_SNAKE_CASE				)


if __name__ == "__main__":
 main()






import functools






def _lowerCamelCase  (		snake_case     , snake_case  ):

							# Validation
							if not isinstance(snake_case     , snake_case  ) or not all(isinstance(snake_case     , snake_case  ) for day in days  ):
														raise ValueError('The parameter days should be a list of integers'  )

							if len(snake_case  ) != 3 or not all(isinstance(snake_case     , snake_case  ) for cost in costs  ):
														raise ValueError('The parameter costs should be a list of three integers'  )

							if len(snake_case  ) == 0:
														return 0

							if min(snake_case  ) <= 0:
														raise ValueError('All days elements should be greater than 0'  )

							if max(snake_case  ) >= 366:
														raise ValueError('All days elements should be less than 366'  )

							_lowerCAmelCase							=							set(snake_case  )

							@functools.cache
							def dynamic_programming(snake_case  ) -> int:
														if index > 365:
																					return 0

														if index not in days_set:
																					return dynamic_programming(index + 1  )

														return min(
														    costs[0] + dynamic_programming(index + 1  )     , costs[1] + dynamic_programming(index + 7  )     , costs[2] + dynamic_programming(index + 30  )     , )

							return dynamic_programming(1  )


if __name__ == "__main__":
				import doctest

				doctest.testmod()






