




class 			_lowerCamelCase    :

      """simple docstring"""

      def __init__(  self       :			Optional[Any]			,							snake_case       :			int					):
          __UpperCamelCase			=    data
          __UpperCamelCase			=    42
          __UpperCamelCase			=    42







def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						None:

    """simple docstring"""


    __UpperCamelCase			=    0
    __UpperCamelCase			=    x




def        __SCREAMING_SNAKE_CASE (	lowercase_       ,  lowercase_   )							->						None:

    """simple docstring"""


    __UpperCamelCase		,   __UpperCamelCase			=    find_set(lowercase_   ), find_set(lowercase_   )
    if x == y:
        return

    elif x.rank > y.rank:
        __UpperCamelCase			=    x
    else:
        __UpperCamelCase			=    y
        if x.rank == y.rank:
            y.rank += 1




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						Node:

    """simple docstring"""


    if x != x.parent:
        __UpperCamelCase			=    find_set(x.parent   )
    return x.parent




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						set:

    """simple docstring"""


    __UpperCamelCase			=    ({0, 1, 2}, {3, 4, 5})
    for s in sets:
        if node.data in s:
            return s
    __UpperCamelCase			=    F"{node.data} is not in {sets}"
    raise ValueError(lowercase_   )




def        __SCREAMING_SNAKE_CASE (	)							->						None:

    """simple docstring"""


    __UpperCamelCase			=    [Node(lowercase_   ) for i in range(6   )]
    for v in vertex:
        make_set(lowercase_   )

    union_set(vertex[0]       ,  vertex[1]   )
    union_set(vertex[1]       ,  vertex[2]   )
    union_set(vertex[3]       ,  vertex[4]   )
    union_set(vertex[3]       ,  vertex[5]   )

    for nodea in vertex:
        for nodea in vertex:
            if find_python_set(lowercase_   ).isdisjoint(find_python_set(lowercase_   )   ):
                assert find_set(lowercase_   ) != find_set(lowercase_   )
            else:
                assert find_set(lowercase_   ) == find_set(lowercase_   )


if __name__ == "__main__":
 test_disjoint_set()







from __future__ import annotations







def     A__	(       __A ,			__A						):







    '''simple docstring'''
    _lowerCamelCase  :		List[str]			    =    [None] * (len(__A						) + len(__A						))

    _lowerCamelCase  :		Optional[int]			    =    0  # pointer to current index for left Half
    _lowerCamelCase  :		List[str]			    =    0  # pointer to current index for the right Half
    _lowerCamelCase  :		List[str]			    =    0  # pointer to current index for the sorted array Half

    while pointera < len(__A						) and pointera < len(__A						):
        if left_half[pointera] < right_half[pointera]:
            _lowerCamelCase  :		Optional[Any]			    =    left_half[pointera]
            pointera += 1
            index += 1
        else:
            _lowerCamelCase  :		List[Any]			    =    right_half[pointera]
            pointera += 1
            index += 1
    while pointera < len(__A						):
        _lowerCamelCase  :		int			    =    left_half[pointera]
        pointera += 1
        index += 1

    while pointera < len(__A						):
        _lowerCamelCase  :		Optional[Any]			    =    right_half[pointera]
        pointera += 1
        index += 1

    return sorted_array







def     A__	(       __A						):







    '''simple docstring'''
    if len(__A						) <= 1:
        return array
    # the actual formula to calculate the middle element = left + (right - left) // 2
    # this avoids integer overflow in case of large N
    _lowerCamelCase  :		int			    =    0 + (len(__A						) - 0) // 2

    # Split the array into halves till the array length becomes equal to One
    # merge the arrays of single length returned by mergeSort function and
    # pass them into the merge arrays function which merges the array
    _lowerCamelCase  :		List[str]			    =    array[:middle]
    _lowerCamelCase  :		Optional[int]			    =    array[middle:]

    return merge(merge_sort(__A						) ,			merge_sort(__A						)						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()




