
from itertools import permutations





def        lowerCAmelCase       (				snake_case__   :      int = 5 )->			int:
    if gon_side < 3 or gon_side > 5:
        raise ValueError("gon_side must be in the range [3, 5]" )

    # Since it's 16, we know 10 is on the outer ring
    # Put the big numbers at the end so that they are never the first number
    A_								=					list(range(gon_side + 1				,					0				,					-1 ) )
    A_								=					list(range(gon_side + 2				,					gon_side * 2 + 1 ) )

    for perm in permutations(small_numbers + big_numbers ):
        A_								=					generate_gon_ring(snake_case__				,					list(snake_case__ ) )
        if is_magic_gon(snake_case__ ):
            return int("".join(str(snake_case__ ) for n in numbers ) )

    A_								=					f'Magic {gon_side}-gon ring is impossible'
    raise ValueError(snake_case__ )





def        lowerCAmelCase       (				snake_case__   :      int				,					snake_case__   :      list[int] )->			list[int]:
    A_								=					[0] * (gon_side * 3)
    A_								=					perm[0:3]
    perm.append(perm[1] )

    A_								=					1 if gon_side < 5 else 2

    for i in range(1				,					len(snake_case__ ) // 3 + magic_number ):
        A_								=					perm[2 * i + 1]
        A_								=					result[3 * i - 1]
        A_								=					perm[2 * i + 2]

    return result





def        lowerCAmelCase       (				snake_case__   :      list[int] )->			bool:
    if len(snake_case__ ) % 3 != 0:
        raise ValueError("a gon ring should have a length that is a multiple of 3" )

    if min(numbers[::3] ) != numbers[0]:
        return False

    A_								=					sum(numbers[:3] )

    return all(sum(numbers[i : i + 3] ) == total for i in range(3				,					len(snake_case__ )				,					3 ) )


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








import colorsys
import io

import cva
import matplotlib as mpl
import matplotlib.colors as mplc
import matplotlib.figure as mplfigure
import numpy as np
import torch
from matplotlib.backends.backend_agg import FigureCanvasAgg

from utils import img_tensorize


__magic_name__  :  Dict     			=   1_0_0_0


class 							lowerCamelCase       :



  """simple docstring"""





  def __init__(					self						,    __UpperCamelCase						,    __UpperCamelCase=1.2						,    __UpperCamelCase="g"						,    __UpperCamelCase=0.5						,    __UpperCamelCase="-"						,    __UpperCamelCase="test_out.jpg"						,    __UpperCamelCase=True						,    __UpperCamelCase=False						,    __UpperCamelCase=None						,    __UpperCamelCase=None						,    __UpperCamelCase=0.7						,    ):
      if isinstance(__UpperCamelCase						,    torch.Tensor					):
          A_								=					img.numpy().astype("np.uint8"					)
      if isinstance(__UpperCamelCase						,    __UpperCamelCase					):
          A_								=					img_tensorize(__UpperCamelCase					)
      assert isinstance(__UpperCamelCase						,    np.ndarray					)

      A_	,	A_								=					img.shape[1], img.shape[0]
      A_								=					mplfigure.Figure(frameon=__UpperCamelCase					)
      A_								=					fig.get_dpi()
      A_								=					(width * scale + 1E-2) / dpi
      A_								=					(height * scale + 1E-2) / dpi
      fig.set_size_inches(__UpperCamelCase						,    __UpperCamelCase					)
      A_								=					fig.add_axes([0.0, 0.0, 1.0, 1.0]					)
      ax.axis("off"					)
      ax.set_xlim(0.0						,    __UpperCamelCase					)
      ax.set_ylim(__UpperCamelCase					)

      A_								=					saveas
      A_								=					rgb
      A_								=					pynb
      A_								=					img
      A_								=					edgecolor
      A_								=					0.5
      A_								=					linestyle
      A_								=					int(np.sqrt(min(__UpperCamelCase						,    __UpperCamelCase					)					) * scale // 3					)
      A_								=					width
      A_								=					height
      A_								=					scale
      A_								=					fig
      A_								=					ax
      A_								=					pad
      A_								=					idaobj
      A_								=					idaattr
      A_								=					FigureCanvasAgg(__UpperCamelCase					)

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase=None					):
      if color is None:
          A_								=					self.edgecolor
      ((A_)	,	(A_)	,	(A_)	,	(A_))								=					box
      A_								=					xa - xa
      A_								=					ya - ya
      self.ax.add_patch(
          mpl.patches.Rectangle(
              (xa, ya)						,    __UpperCamelCase						,    __UpperCamelCase						,    fill=__UpperCamelCase						,    edgecolor=__UpperCamelCase						,    linewidth=self.font_size // 3						,    alpha=self.alpha						,    linestyle=self.linestyle						,    )					)

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase=None						,    __UpperCamelCase=None						,    __UpperCamelCase=None						,    __UpperCamelCase=None					):
      if len(boxes.shape					) > 2:
          A_								=					boxes[0]
      if len(obj_ids.shape					) > 1:
          A_								=					obj_ids[0]
      if len(obj_scores.shape					) > 1:
          A_								=					obj_scores[0]
      if len(attr_ids.shape					) > 1:
          A_								=					attr_ids[0]
      if len(attr_scores.shape					) > 1:
          A_								=					attr_scores[0]
      if isinstance(__UpperCamelCase						,    torch.Tensor					):
          A_								=					boxes.numpy()
      if isinstance(__UpperCamelCase						,    __UpperCamelCase					):
          A_								=					np.array(__UpperCamelCase					)
      assert isinstance(__UpperCamelCase						,    np.ndarray					)
      A_								=					np.prod(boxes[:, 2:] - boxes[:, :2]						,    axis=1					)
      A_								=					np.argsort(-areas					).tolist()
      A_								=					boxes[sorted_idxs] if boxes is not None else None
      A_								=					obj_ids[sorted_idxs] if obj_ids is not None else None
      A_								=					obj_scores[sorted_idxs] if obj_scores is not None else None
      A_								=					attr_ids[sorted_idxs] if attr_ids is not None else None
      A_								=					attr_scores[sorted_idxs] if attr_scores is not None else None

      A_								=					[self._random_color(maximum=1					) for _ in range(len(__UpperCamelCase					)					)]
      A_								=					[assigned_colors[idx] for idx in sorted_idxs]
      if obj_ids is not None:
          A_								=					self._create_text_labels_attr(__UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase					)
          for i in range(len(__UpperCamelCase					)					):
              A_								=					assigned_colors[i]
              self.add_box(boxes[i]						,    __UpperCamelCase					)
              self.draw_labels(labels[i]						,    boxes[i]						,    __UpperCamelCase					)

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase					):
      A_	,	A_	,	A_	,	A_								=					box
      A_								=					(xa, ya)
      A_								=					(ya - ya) * (xa - xa)
      A_								=					_SMALL_OBJ * self.scale
      if instance_area < small or ya - ya < 40 * self.scale:
          if ya >= self.height - 5:
              A_								=					(xa, ya)
          else:
              A_								=					(xa, ya)

      A_								=					(ya - ya) / np.sqrt(self.height * self.width					)
      A_								=					self._change_color_brightness(__UpperCamelCase						,    brightness_factor=0.7					)
      A_								=					np.clip((height_ratio - 0.02) / 0.08 + 1						,    1.2						,    2					)
      font_size *= 0.75 * self.font_size

      self.draw_text(
          text=__UpperCamelCase						,    position=__UpperCamelCase						,    color=__UpperCamelCase						,    )

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase="g"						,    __UpperCamelCase="left"						,    ):
      A_								=					0
      A_								=					self.font_size
      A_								=					np.maximum(list(mplc.to_rgb(__UpperCamelCase					)					)						,    0.2					)
      A_								=					max(0.8						,    np.max(__UpperCamelCase					)					)
      A_								=					{
          "facecolor": "black",
          "alpha": self.alpha,
          "pad": self.pad,
          "edgecolor": "none",
      }
      A_	,	A_								=					position
      self.ax.text(
          __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase						,    size=font_size * self.scale						,    family="sans-serif"						,    bbox=__UpperCamelCase						,    verticalalignment="top"						,    horizontalalignment=__UpperCamelCase						,    color=__UpperCamelCase						,    zorder=10						,    rotation=__UpperCamelCase						,    )

  def 					lowercase_						(					self						,    __UpperCamelCase=None					):
      if saveas is None:
          A_								=					self.saveas
      if saveas.lower().endswith(".jpg"					) or saveas.lower().endswith(".png"					):
          cva.imwrite(
              __UpperCamelCase						,    self._get_buffer()[:, :, ::-1]						,    )
      else:
          self.fig.savefig(__UpperCamelCase					)

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase					):
      A_								=					[self.idaobj[i] for i in classes]
      A_								=					[self.idaattr[i] for i in attr_classes]
      A_								=					[
          f'{label} {score:.2f} {attr} {attr_score:.2f}'
          for label, score, attr, attr_score in zip(__UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase						,    __UpperCamelCase					)
      ]
      return labels

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase					):
      A_								=					[self.idaobj[i] for i in classes]
      if scores is not None:
          if labels is None:
              A_								=					["{:.0f}%".format(s * 100					) for s in scores]
          else:
              A_								=					["{} {:.0f}%".format(__UpperCamelCase						,    s * 100					) for li, s in zip(__UpperCamelCase						,    __UpperCamelCase					)]
      return labels

  def 					lowercase_						(					self						,    __UpperCamelCase=255					):
      A_								=					np.random.randint(0						,    len(_COLORS					)					)
      A_								=					_COLORS[idx] * maximum
      if not self.rgb:
          A_								=					ret[::-1]
      return ret

  def 					lowercase_						(					self					):
      if not self.pynb:
          A_	,	A_								=					self.canvas.print_to_buffer()
          if (width, height) != (self.width, self.height):
              A_								=					cva.resize(self.img						,    (width, height)					)
          else:
              A_								=					self.img
      else:
          A_								=					io.BytesIO()  # works for cairo backend
          self.canvas.print_rgba(__UpperCamelCase					)
          A_	,	A_								=					self.width, self.height
          A_								=					buf.getvalue()
          A_								=					self.img

      A_								=					np.frombuffer(__UpperCamelCase						,    dtype="uint8"					)
      A_								=					buffer.reshape(__UpperCamelCase						,    __UpperCamelCase						,    4					)
      A_	,	A_								=					np.split(__UpperCamelCase						,    [3]						,    axis=2					)

      try:
          import numexpr as ne  # fuse them with numexpr

          A_								=					ne.evaluate("img * (1 - alpha / 255.0) + rgb * (alpha / 255.0)"					)
      except ImportError:
          A_								=					alpha.astype("float32"					) / 255.0
          A_								=					img * (1 - alpha) + rgb * alpha

      return visualized_image.astype("uint8"					)

  def 					lowercase_						(					self						,    __UpperCamelCase						,    __UpperCamelCase					):
      assert brightness_factor >= -1.0 and brightness_factor <= 1.0
      A_								=					mplc.to_rgb(__UpperCamelCase					)
      A_								=					colorsys.rgb_to_hls(*mplc.to_rgb(__UpperCamelCase					)					)
      A_								=					polygon_color[1] + (brightness_factor * polygon_color[1])
      A_								=					0.0 if modified_lightness < 0.0 else modified_lightness
      A_								=					1.0 if modified_lightness > 1.0 else modified_lightness
      A_								=					colorsys.hls_to_rgb(polygon_color[0]						,    __UpperCamelCase						,    polygon_color[2]					)
      return modified_color



__magic_name__  :  List[str]     			=   (
    np.array(
        [
            0.000,
            0.447,
            0.741,
            0.850,
            0.325,
            0.098,
            0.929,
            0.694,
            0.125,
            0.494,
            0.184,
            0.556,
            0.466,
            0.674,
            0.188,
            0.301,
            0.745,
            0.933,
            0.635,
            0.078,
            0.184,
            0.300,
            0.300,
            0.300,
            0.600,
            0.600,
            0.600,
            1.000,
            0.000,
            0.000,
            1.000,
            0.500,
            0.000,
            0.749,
            0.749,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            1.000,
            0.667,
            0.000,
            1.000,
            0.333,
            0.333,
            0.000,
            0.333,
            0.667,
            0.000,
            0.333,
            1.000,
            0.000,
            0.667,
            0.333,
            0.000,
            0.667,
            0.667,
            0.000,
            0.667,
            1.000,
            0.000,
            1.000,
            0.333,
            0.000,
            1.000,
            0.667,
            0.000,
            1.000,
            1.000,
            0.000,
            0.000,
            0.333,
            0.500,
            0.000,
            0.667,
            0.500,
            0.000,
            1.000,
            0.500,
            0.333,
            0.000,
            0.500,
            0.333,
            0.333,
            0.500,
            0.333,
            0.667,
            0.500,
            0.333,
            1.000,
            0.500,
            0.667,
            0.000,
            0.500,
            0.667,
            0.333,
            0.500,
            0.667,
            0.667,
            0.500,
            0.667,
            1.000,
            0.500,
            1.000,
            0.000,
            0.500,
            1.000,
            0.333,
            0.500,
            1.000,
            0.667,
            0.500,
            1.000,
            1.000,
            0.500,
            0.000,
            0.333,
            1.000,
            0.000,
            0.667,
            1.000,
            0.000,
            1.000,
            1.000,
            0.333,
            0.000,
            1.000,
            0.333,
            0.333,
            1.000,
            0.333,
            0.667,
            1.000,
            0.333,
            1.000,
            1.000,
            0.667,
            0.000,
            1.000,
            0.667,
            0.333,
            1.000,
            0.667,
            0.667,
            1.000,
            0.667,
            1.000,
            1.000,
            1.000,
            0.000,
            1.000,
            1.000,
            0.333,
            1.000,
            1.000,
            0.667,
            1.000,
            0.333,
            0.000,
            0.000,
            0.500,
            0.000,
            0.000,
            0.667,
            0.000,
            0.000,
            0.833,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            0.167,
            0.000,
            0.000,
            0.333,
            0.000,
            0.000,
            0.500,
            0.000,
            0.000,
            0.667,
            0.000,
            0.000,
            0.833,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            0.167,
            0.000,
            0.000,
            0.333,
            0.000,
            0.000,
            0.500,
            0.000,
            0.000,
            0.667,
            0.000,
            0.000,
            0.833,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            0.143,
            0.143,
            0.143,
            0.857,
            0.857,
            0.857,
            1.000,
            1.000,
            1.000,
        ]
    )
    .astype(np.floataa)
    .reshape(-1, 3)
)






