
"""simple docstring"""

from functools import lru_cache




def     lowercase__						(					lowerCAmelCase				:					int ) ->      set:






    """simple docstring"""




    UpperCAmelCase									=					2
    UpperCAmelCase									=					set()
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.add(lowerCAmelCase )
    if n > 1:
        factors.add(lowerCAmelCase )
    return factors




@lru_cache
def     lowercase__						(					lowerCAmelCase				:					int ) ->      int:






    """simple docstring"""




    return len(unique_prime_factors(lowerCAmelCase ) )




def     lowercase__						(					lowerCAmelCase				:					list ) ->      bool:






    """simple docstring"""




    return len(set(lowerCAmelCase ) ) in (0, 1)




def     lowercase__						(					lowerCAmelCase				:					int ) ->      list:






    """simple docstring"""




    UpperCAmelCase									=					2

    while True:
        # Increment each value of a generated range
        UpperCAmelCase									=					[base + i for i in range(lowerCAmelCase )]

        # Run elements through out unique_prime_factors function
        # Append our target number to the end.
        UpperCAmelCase									=					[upf_len(lowerCAmelCase ) for x in group]
        checker.append(lowerCAmelCase )

        # If all numbers in the list are equal, return the group variable.
        if equality(lowerCAmelCase ):
            return group

        # Increment our base variable by 1
        base += 1




def     lowercase__						(					lowerCAmelCase				:					int = 4 ) ->      int:






    """simple docstring"""




    UpperCAmelCase									=					run(lowerCAmelCase )
    return results[0] if len(lowerCAmelCase ) else None


if __name__ == "__main__":
   print(solution())





"""simple docstring"""

def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      int:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )
    if n == 0:
        return 0
    UpperCAmelCase									=					float('-inf' )
    for i in range(1 ,				n + 1 ):
        UpperCAmelCase									=					max(
            lowerCAmelCase ,				prices[i - 1] + naive_cut_rod_recursive(n - i ,				lowerCAmelCase ) )

    return max_revue




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Dict:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					[float('-inf' ) for _ in range(n + 1 )]
    return _top_down_cut_rod_recursive(lowerCAmelCase ,				lowerCAmelCase ,				lowerCAmelCase )




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ,				lowerCAmelCase				:					list ) ->      int:






    """simple docstring"""




    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        UpperCAmelCase									=					float('-inf' )
        for i in range(1 ,				n + 1 ):
            UpperCAmelCase									=					max(
                lowerCAmelCase ,				prices[i - 1] + _top_down_cut_rod_recursive(n - i ,				lowerCAmelCase ,				lowerCAmelCase ) ,				)

        UpperCAmelCase									=					max_revenue

    return max_rev[n]




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Optional[int]:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )

    # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
    # length 0.
    UpperCAmelCase									=					[float('-inf' ) for _ in range(n + 1 )]
    UpperCAmelCase									=					0

    for i in range(1 ,				n + 1 ):
        UpperCAmelCase									=					max_rev[i]
        for j in range(1 ,				i + 1 ):
            UpperCAmelCase									=					max(lowerCAmelCase ,				prices[j - 1] + max_rev[i - j] )

        UpperCAmelCase									=					max_revenue_i

    return max_rev[n]




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Union[str, Any]:






    """simple docstring"""




    if n < 0:
        UpperCAmelCase									=					F"n must be greater than or equal to 0. Got n = {n}"
        raise ValueError(lowerCAmelCase )

    if n > len(lowerCAmelCase ):
        UpperCAmelCase									=					(
            'Each integral piece of rod must have a corresponding price. '
            F"Got n = {n} but length of prices = {len(lowerCAmelCase )}"
        )
        raise ValueError(lowerCAmelCase )




def     lowercase__						(					) ->      Optional[int]:






    """simple docstring"""




    UpperCAmelCase									=					[6, 10, 12, 15, 20, 23]
    UpperCAmelCase									=					len(lowerCAmelCase )

    # the best revenue comes from cutting the rod into 6 pieces, each
    # of length 1 resulting in a revenue of 6 * 6 = 36.
    UpperCAmelCase									=					36

    UpperCAmelCase									=					top_down_cut_rod(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					bottom_up_cut_rod(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					naive_cut_rod_recursive(lowerCAmelCase ,				lowerCAmelCase )

    assert expected_max_revenue == max_rev_top_down
    assert max_rev_top_down == max_rev_bottom_up
    assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
   main()



