
"""simple docstring"""
def  lowercase     ():
						for n in range(1 ,    100_0000						):
												yield n * (n + 1) // 2

def  lowercase     (_lowerCAmelCase						):
						__lowerCAmelCase     =  1
						__lowerCAmelCase     =  2
						while i * i <= n:
												__lowerCAmelCase     =  0
												while n % i == 0:
																		n //= i
																		multiplicity += 1
												divisors_count *= multiplicity + 1
												i += 1
						if n > 1:
												divisors_count *= 2
						return divisors_count

def  lowercase     ():
						return next(i for i in triangle_number_generator() if count_divisors(_lowerCAmelCase						) > 500						)


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


"""simple docstring"""
import io
import math
from typing import Dict, Optional, Union

import numpy as np
from huggingface_hub import hf_hub_download

from ...image_processing_utils import BaseImageProcessor, BatchFeature
from ...image_transforms import convert_to_rgb, normalize, to_channel_dimension_format, to_pil_image
from ...image_utils import (
    ChannelDimension,
    ImageInput,
    get_image_size,
    infer_channel_dimension_format,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_torch_available, is_vision_available, logging
from ...utils.import_utils import requires_backends


if is_vision_available():
			import textwrap

			from PIL import Image, ImageDraw, ImageFont

if is_torch_available():
			import torch

			from transformers.pytorch_utils import is_torch_greater_or_equal_than_1_11
else:
			SCREAMING_SNAKE_CASE_					     =	False


SCREAMING_SNAKE_CASE_					     =	logging.get_logger(__name__)
SCREAMING_SNAKE_CASE_					     =	'''ybelkada/fonts'''

def  lowercase     ():
						if is_torch_available() and not is_torch_greater_or_equal_than_1_11:
												raise ImportError(
												    f"""You are using torch=={torch.__version__}, but torch>=1.11.0 is required to use """
												    """Pix2StructImageProcessor. Please upgrade torch."""						)

def  lowercase     (_lowerCAmelCase ,    _lowerCAmelCase ,    _lowerCAmelCase						):
						requires_backends(_lowerCAmelCase ,    ["""torch"""]						)
						_check_torch_version()

						__lowerCAmelCase     =  image_tensor.unsqueeze(0						)
						__lowerCAmelCase     =  torch.nn.functional.unfold(_lowerCAmelCase ,    (patch_height, patch_width) ,    stride=(patch_height, patch_width)						)
						__lowerCAmelCase     =  patches.reshape(image_tensor.size(0						) ,    image_tensor.size(1						) ,    _lowerCAmelCase ,    _lowerCAmelCase ,    -1						)
						__lowerCAmelCase     =  patches.permute(0 ,    4 ,    2 ,    3 ,    1						).reshape(
						    image_tensor.size(2						) // patch_height ,    image_tensor.size(3						) // patch_width ,    image_tensor.size(1						) * patch_height * patch_width ,    )
						return patches.unsqueeze(0						)

def  lowercase     (_lowerCAmelCase ,    _lowerCAmelCase = 36 ,    _lowerCAmelCase = "black" ,    _lowerCAmelCase = "white" ,    _lowerCAmelCase = 5 ,    _lowerCAmelCase = 5 ,    _lowerCAmelCase = 5 ,    _lowerCAmelCase = 5 ,    _lowerCAmelCase = None ,    _lowerCAmelCase = None ,    ):
						requires_backends(_lowerCAmelCase ,    """vision"""						)
						# Add new lines so that each line is no more than 80 characters.

						__lowerCAmelCase     =  textwrap.TextWrapper(width=80						)
						__lowerCAmelCase     =  wrapper.wrap(text=_lowerCAmelCase						)
						__lowerCAmelCase     =  """\n""".join(_lowerCAmelCase						)

						if font_bytes is not None and font_path is None:
												__lowerCAmelCase     =  io.BytesIO(_lowerCAmelCase						)
						elif font_path is not None:
												__lowerCAmelCase     =  font_path
						else:
												__lowerCAmelCase     =  hf_hub_download(_lowerCAmelCase ,    """Arial.TTF"""						)
						__lowerCAmelCase     =  ImageFont.truetype(_lowerCAmelCase ,    encoding="""UTF-8""" ,    size=_lowerCAmelCase						)

						# Use a temporary canvas to determine the width and height in pixels when
						# rendering the text.
						__lowerCAmelCase     =  ImageDraw.Draw(Image.new("""RGB""" ,    (1, 1) ,    _lowerCAmelCase						)						)
						__lowerCAmelCase   ,     __lowerCAmelCase   ,     __lowerCAmelCase   ,     __lowerCAmelCase     =  temp_draw.textbbox((0, 0) ,    _lowerCAmelCase ,    _lowerCAmelCase						)

						# Create the actual image with a bit of padding around the text.
						__lowerCAmelCase     =  text_width + left_padding + right_padding
						__lowerCAmelCase     =  text_height + top_padding + bottom_padding
						__lowerCAmelCase     =  Image.new("""RGB""" ,    (image_width, image_height) ,    _lowerCAmelCase						)
						__lowerCAmelCase     =  ImageDraw.Draw(_lowerCAmelCase						)
						draw.text(xy=(left_padding, top_padding) ,    text=_lowerCAmelCase ,    fill=_lowerCAmelCase ,    font=_lowerCAmelCase						)
						return image

def  lowercase     (_lowerCAmelCase ,    _lowerCAmelCase ,    **_lowerCAmelCase						):
						requires_backends(_lowerCAmelCase ,    """vision"""						)

						# Convert to PIL image if necessary
						__lowerCAmelCase     =  to_pil_image(_lowerCAmelCase						)

						__lowerCAmelCase     =  render_text(_lowerCAmelCase ,    **_lowerCAmelCase						)
						__lowerCAmelCase     =  max(header_image.width ,    image.width						)

						__lowerCAmelCase     =  int(image.height * (new_width / image.width)						)
						__lowerCAmelCase     =  int(header_image.height * (new_width / header_image.width)						)

						__lowerCAmelCase     =  Image.new("""RGB""" ,    (new_width, new_height + new_header_height) ,    """white"""						)
						new_image.paste(header_image.resize((new_width, new_header_height)						) ,    (0, 0)						)
						new_image.paste(image.resize((new_width, new_height)						) ,    (0, new_header_height)						)

						# Convert back to the original framework if necessary
						__lowerCAmelCase     =  to_numpy_array(_lowerCAmelCase						)

						if infer_channel_dimension_format(_lowerCAmelCase						) == ChannelDimension.LAST:
												__lowerCAmelCase     =  to_channel_dimension_format(_lowerCAmelCase ,    ChannelDimension.LAST						)

						return new_image



class       lowerCAmelCase_		(				A__ ):



							'''simple docstring'''





							_snake_case						      =		['''flattened_patches''']




							def __init__( self    ,				snake_case_ = True    ,				snake_case_ = True    ,				snake_case_ = None    ,				snake_case_ = 2_048    ,				snake_case_ = False    ,				**snake_case_    ,				)       ->  None:
													super().__init__(**snake_case_				)
													__lowerCAmelCase     =  patch_size if patch_size is not None else {"""height""": 16, """width""": 16}
													__lowerCAmelCase     =  do_normalize
													__lowerCAmelCase     =  do_convert_rgb
													__lowerCAmelCase     =  max_patches
													__lowerCAmelCase     =  is_vqa




							def    A__						( self    ,				snake_case_    ,				snake_case_    ,				snake_case_    ,				**snake_case_				)       ->  np.ndarray:
													requires_backends(self.extract_flattened_patches    ,				"""torch"""				)
													_check_torch_version()

													# convert to torch
													__lowerCAmelCase     =  to_channel_dimension_format(snake_case_    ,				ChannelDimension.FIRST				)
													__lowerCAmelCase     =  torch.from_numpy(snake_case_				)

													__lowerCAmelCase   ,     __lowerCAmelCase     =  patch_size["""height"""], patch_size["""width"""]
													__lowerCAmelCase   ,     __lowerCAmelCase     =  get_image_size(snake_case_				)

													# maximize scale s.t.
													__lowerCAmelCase     =  math.sqrt(max_patches * (patch_height / image_height) * (patch_width / image_width)				)
													__lowerCAmelCase     =  max(min(math.floor(scale * image_height / patch_height				)    ,				snake_case_				)    ,				1				)
													__lowerCAmelCase     =  max(min(math.floor(scale * image_width / patch_width				)    ,				snake_case_				)    ,				1				)
													__lowerCAmelCase     =  max(num_feasible_rows * patch_height    ,				1				)
													__lowerCAmelCase     =  max(num_feasible_cols * patch_width    ,				1				)

													__lowerCAmelCase     =  torch.nn.functional.interpolate(
													    image.unsqueeze(0				)    ,				size=(resized_height, resized_width)    ,				mode="""bilinear"""    ,				align_corners=snake_case_    ,				antialias=snake_case_    ,				).squeeze(0				)

													# [1, rows, columns, patch_height * patch_width * image_channels]
													__lowerCAmelCase     =  torch_extract_patches(snake_case_    ,				snake_case_    ,				snake_case_				)

													__lowerCAmelCase     =  patches.shape
													__lowerCAmelCase     =  patches_shape[1]
													__lowerCAmelCase     =  patches_shape[2]
													__lowerCAmelCase     =  patches_shape[3]

													# [rows * columns, patch_height * patch_width * image_channels]
													__lowerCAmelCase     =  patches.reshape([rows * columns, depth]				)

													# [rows * columns, 1]
													__lowerCAmelCase     =  torch.arange(snake_case_				).reshape([rows, 1]				).repeat(1    ,				snake_case_				).reshape([rows * columns, 1]				)
													__lowerCAmelCase     =  torch.arange(snake_case_				).reshape([1, columns]				).repeat(snake_case_    ,				1				).reshape([rows * columns, 1]				)

													# Offset by 1 so the ids do not contain zeros, which represent padding.
													row_ids += 1
													col_ids += 1

													# Prepare additional patch features.
													# [rows * columns, 1]
													__lowerCAmelCase     =  row_ids.to(torch.floataa				)
													__lowerCAmelCase     =  col_ids.to(torch.floataa				)

													# [rows * columns, 2 + patch_height * patch_width * image_channels]
													__lowerCAmelCase     =  torch.cat([row_ids, col_ids, patches]    ,				-1				)

													# [max_patches, 2 + patch_height * patch_width * image_channels]
													__lowerCAmelCase     =  torch.nn.functional.pad(snake_case_    ,				[0, 0, 0, max_patches - (rows * columns)]				).float()

													__lowerCAmelCase     =  to_numpy_array(snake_case_				)

													return result




							def    A__						( self    ,				snake_case_    ,				snake_case_ = None    ,				**snake_case_				)       ->  np.ndarray:
													if image.dtype == np.uinta:
																			__lowerCAmelCase     =  image.astype(np.floataa				)

													# take mean across the whole `image`
													__lowerCAmelCase     =  np.mean(snake_case_				)
													__lowerCAmelCase     =  np.std(snake_case_				)
													__lowerCAmelCase     =  max(snake_case_    ,				1.0 / math.sqrt(np.prod(image.shape				)				)				)

													return normalize(snake_case_    ,				mean=snake_case_    ,				std=snake_case_    ,				**snake_case_				)




							def    A__						( self    ,				snake_case_    ,				snake_case_ = None    ,				snake_case_ = None    ,				snake_case_ = None    ,				snake_case_ = None    ,				snake_case_ = None    ,				snake_case_ = None    ,				snake_case_ = ChannelDimension.FIRST    ,				**snake_case_    ,				)       ->  ImageInput:
													__lowerCAmelCase     =  do_normalize if do_normalize is not None else self.do_normalize
													__lowerCAmelCase     =  do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb
													__lowerCAmelCase     =  patch_size if patch_size is not None else self.patch_size
													__lowerCAmelCase     =  max_patches if max_patches is not None else self.max_patches
													__lowerCAmelCase     =  self.is_vqa

													if kwargs.get("""data_format"""    ,				snake_case_				) is not None:
																			raise ValueError("""data_format is not an accepted input as the outputs are """				)

													__lowerCAmelCase     =  make_list_of_images(snake_case_				)

													if not valid_images(snake_case_				):
																			raise ValueError(
																			    """Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, """
																			    """torch.Tensor, tf.Tensor or jax.ndarray."""				)

													# PIL RGBA images are converted to RGB
													if do_convert_rgb:
																			__lowerCAmelCase     =  [convert_to_rgb(snake_case_				) for image in images]

													# All transformations expect numpy arrays.
													__lowerCAmelCase     =  [to_numpy_array(snake_case_				) for image in images]

													if is_vqa:
																			if header_text is None:
																									raise ValueError("""A header text must be provided for VQA models."""				)
																			__lowerCAmelCase     =  kwargs.pop("""font_bytes"""    ,				snake_case_				)
																			__lowerCAmelCase     =  kwargs.pop("""font_path"""    ,				snake_case_				)

																			if isinstance(snake_case_    ,				snake_case_				):
																									__lowerCAmelCase     =  [header_text] * len(snake_case_				)

																			__lowerCAmelCase     =  [
																			    render_header(snake_case_    ,				header_text[i]    ,				font_bytes=snake_case_    ,				font_path=snake_case_				)
																			    for i, image in enumerate(snake_case_				)
																			]

													if do_normalize:
																			__lowerCAmelCase     =  [self.normalize(image=snake_case_				) for image in images]

													# convert to torch tensor and permute
													__lowerCAmelCase     =  [
													    self.extract_flattened_patches(image=snake_case_    ,				max_patches=snake_case_    ,				patch_size=snake_case_				)
													    for image in images
													]

													# create attention mask in numpy
													__lowerCAmelCase     =  [(image.sum(axis=-1				) != 0).astype(np.floataa				) for image in images]

													__lowerCAmelCase     =  BatchFeature(
													    data={"""flattened_patches""": images, """attention_mask""": attention_masks}    ,				tensor_type=snake_case_				)

													return encoded_outputs
