


import sys
from typing import Tuple

import numpy as np
import torch
from PIL import Image
from torch import nn

from transformers.image_utils import PILImageResampling
from utils import img_tensorize


class 		_SCREAMING_SNAKE_CASE    :


     def __init__(     self       ,				A_       ,				A_=sys.maxsize						):
       _UpperCAmelCase		:       List[Any]       =    """bilinear"""
       _UpperCAmelCase		:       Union[str, Any]       =    max_size
       _UpperCAmelCase		:       Dict       =    short_edge_length




     def __call__(     self       ,				A_						):
       _UpperCAmelCase		:       Union[str, Any]       =    []
       for img in imgs:
         _UpperCAmelCase,_UpperCAmelCase		:       str       =    img.shape[:2]
         # later: provide list and randomly choose index for resize
         _UpperCAmelCase		:       str       =    np.random.randint(self.short_edge_length[0]       ,				self.short_edge_length[1] + 1						)
         if size == 0:
           return img
         _UpperCAmelCase		:       Optional[Any]       =    size * 1.0 / min(A_       ,				A_						)
         if h < w:
           _UpperCAmelCase,_UpperCAmelCase		:       Any       =    size, scale * w
         else:
           _UpperCAmelCase,_UpperCAmelCase		:       Tuple       =    scale * h, size
         if max(A_       ,				A_						) > self.max_size:
           _UpperCAmelCase		:       List[str]       =    self.max_size * 1.0 / max(A_       ,				A_						)
           _UpperCAmelCase		:       Tuple       =    newh * scale
           _UpperCAmelCase		:       List[Any]       =    neww * scale
         _UpperCAmelCase		:       Any       =    int(neww + 0.5						)
         _UpperCAmelCase		:       Optional[Any]       =    int(newh + 0.5						)

         if img.dtype == np.uinta:
           _UpperCAmelCase		:       int       =    Image.fromarray(A_						)
           _UpperCAmelCase		:       Any       =    pil_image.resize((neww, newh)       ,				PILImageResampling.BILINEAR						)
           _UpperCAmelCase		:       Optional[int]       =    np.asarray(A_						)
         else:
           _UpperCAmelCase		:       List[str]       =    img.permute(2       ,				0       ,				1						).unsqueeze(0						)  # 3, 0, 1)  # hw(c) -> nchw
           _UpperCAmelCase		:       List[str]       =    nn.functional.interpolate(
               A_       ,				(newh, neww)       ,				mode=self.interp_method       ,				align_corners=A_						).squeeze(0						)
         img_augs.append(A_						)

       return img_augs


class 		_SCREAMING_SNAKE_CASE    :


     def __init__(     self       ,				A_						):
       _UpperCAmelCase		:       Optional[int]       =    ResizeShortestEdge([cfg.INPUT.MIN_SIZE_TEST, cfg.INPUT.MIN_SIZE_TEST]       ,				cfg.INPUT.MAX_SIZE_TEST						)
       _UpperCAmelCase		:       Union[str, Any]       =    cfg.INPUT.FORMAT
       _UpperCAmelCase		:       List[Any]       =    cfg.SIZE_DIVISIBILITY
       _UpperCAmelCase		:       List[str]       =    cfg.PAD_VALUE
       _UpperCAmelCase		:       Tuple       =    cfg.INPUT.MAX_SIZE_TEST
       _UpperCAmelCase		:       Optional[Any]       =    cfg.MODEL.DEVICE
       _UpperCAmelCase		:       Optional[int]       =    torch.tensor(cfg.MODEL.PIXEL_STD						).to(self.device						).view(len(cfg.MODEL.PIXEL_STD						)       ,				1       ,				1						)
       _UpperCAmelCase		:       Optional[Any]       =    torch.tensor(cfg.MODEL.PIXEL_MEAN						).to(self.device						).view(len(cfg.MODEL.PIXEL_STD						)       ,				1       ,				1						)
       _UpperCAmelCase		:       Tuple       =    lambda A_						: (x - self.pixel_mean) / self.pixel_std


     def 					__snake_case(     self       ,				A_						):
       _UpperCAmelCase		:       List[Any]       =    tuple(max(A_						) for s in zip(*[img.shape for img in images]						)						)
       _UpperCAmelCase		:       Optional[int]       =    [im.shape[-2:] for im in images]
       _UpperCAmelCase		:       str       =    [
           nn.functional.pad(
               A_       ,				[0, max_size[-1] - size[1], 0, max_size[-2] - size[0]]       ,				value=self.pad_value       ,				)
           for size, im in zip(A_       ,				A_						)
       ]

       return torch.stack(A_						), torch.tensor(A_						)




     def __call__(     self       ,				A_       ,				A_=False						):
       with torch.no_grad():
         if not isinstance(A_       ,				A_						):
           _UpperCAmelCase		:       Optional[int]       =    [images]
         if single_image:
           assert len(A_						) == 1
         for i in range(len(A_						)						):
           if isinstance(images[i]       ,				torch.Tensor						):
             images.insert(A_       ,				images.pop(A_						).to(self.device						).float()						)
           elif not isinstance(images[i]       ,				torch.Tensor						):
             images.insert(
                 A_       ,				torch.as_tensor(img_tensorize(images.pop(A_						)       ,				input_format=self.input_format						)						)
                 .to(self.device						)
                 .float()       ,				)
            # resize smallest edge
         _UpperCAmelCase		:       Any       =    torch.tensor([im.shape[:2] for im in images]						)
         _UpperCAmelCase		:       str       =    self.aug(A_						)
         # transpose images and convert to torch tensors
         # images = [torch.as_tensor(i.astype("float32")).permute(2, 0, 1).to(self.device) for i in images]
         # now normalize before pad to avoid useless arithmetic
         _UpperCAmelCase		:       Any       =    [self.normalizer(A_						) for x in images]
         # now pad them to do the following operations
         _UpperCAmelCase,_UpperCAmelCase		:       str       =    self.pad(A_						)
         # Normalize

         if self.size_divisibility > 0:
           raise NotImplementedError()
         # pad
         _UpperCAmelCase		:       Optional[Any]       =    torch.true_divide(A_       ,				A_						)
         if single_image:
           return images[0], sizes[0], scales_yx[0]
         else:
           return images, sizes, scales_yx




def       a__						(		snake_case__				:       List[str]	,      snake_case__				:       Optional[int]    ):
  boxes[:, 0::2] *= scale_yx[:, 1]
  boxes[:, 1::2] *= scale_yx[:, 0]
  return boxes





def       a__						(		snake_case__				:       str	,      snake_case__				:       Tuple[int, int]    ):
  assert torch.isfinite(snake_case__    ).all(), "Box tensor contains infinite or NaN!"
  _UpperCAmelCase,_UpperCAmelCase		:       Optional[int]       =    box_size
  tensor[:, 0].clamp_(min=0	,      max=snake_case__    )
  tensor[:, 1].clamp_(min=0	,      max=snake_case__    )
  tensor[:, 2].clamp_(min=0	,      max=snake_case__    )
  tensor[:, 3].clamp_(min=0	,      max=snake_case__    )









from itertools import count
from math import asin, pi, sqrt




def       a__						(		snake_case__				:       float    ):
  return (
      (1 - 2 * point) * sqrt(point - point**2    ) + 2 * point + asin(sqrt(1 - point    )    )
  ) / 4




def       a__						(		snake_case__				:       int    ):
  _UpperCAmelCase		:       int       =    (circles_number + 1 - sqrt(2 * circles_number    )) / (
      2 * (circles_number**2 + 1)
  )
  _UpperCAmelCase		:       Union[str, Any]       =    circles_number * intersection_y

  _UpperCAmelCase		:       Tuple       =    intersection_x * intersection_y / 2
  _UpperCAmelCase		:       str       =    circle_bottom_arc_integral(
      1 / 2    ) - circle_bottom_arc_integral(snake_case__    )

  return triangle_area + concave_region_area




def       a__						(		snake_case__				:       float = 1 / 1000    ):
  _UpperCAmelCase		:       Dict       =    (1 - pi / 4) / 4

  for n in count(1    ):
    if concave_triangle_area(snake_case__    ) / l_section_area < fraction:
      return n

  return -1


if __name__ == "__main__":
 print(F'{solution() = }')





