
import math

class 		lowercase_       :

 def __init__(      self     ,	__UpperCamelCase     ):




        """simple docstring"""


        UpperCamelCase_							       =       len(__UpperCamelCase     )
        UpperCamelCase_							       =       [0] * (
            4 * self.N
        )  # approximate the overall size of segment tree with array N
        self.build(1     ,	0     ,	self.N - 1     )

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ):




        """simple docstring"""


        return idx * 2

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ):




        """simple docstring"""


        return idx * 2 + 1

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ):  # noqa: E741




        """simple docstring"""


        if l == r:
               UpperCamelCase_							       =       A[l]
        else:
               UpperCamelCase_							       =       (l + r) // 2
               self.build(self.left(__UpperCamelCase     )     ,	__UpperCamelCase     ,	__UpperCamelCase     )
               self.build(self.right(__UpperCamelCase     )     ,	mid + 1     ,	__UpperCamelCase     )
               UpperCamelCase_							       =       max(self.st[self.left(__UpperCamelCase     )]     ,	self.st[self.right(__UpperCamelCase     )]     )

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ):




        """simple docstring"""


        return self.update_recursive(1     ,	0     ,	self.N - 1     ,	a - 1     ,	b - 1     ,	__UpperCamelCase     )

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ):  # noqa: E741




        """simple docstring"""


        if r < a or l > b:
               return True
        if l == r:
               UpperCamelCase_							       =       val
               return True
        UpperCamelCase_							       =       (l + r) // 2
        self.update_recursive(self.left(__UpperCamelCase     )     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     )
        self.update_recursive(self.right(__UpperCamelCase     )     ,	mid + 1     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     )
        UpperCamelCase_							       =       max(self.st[self.left(__UpperCamelCase     )]     ,	self.st[self.right(__UpperCamelCase     )]     )
        return True

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase     ):




        """simple docstring"""


        return self.query_recursive(1     ,	0     ,	self.N - 1     ,	a - 1     ,	b - 1     )

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ):  # noqa: E741




        """simple docstring"""


        if r < a or l > b:
               return -math.inf
        if l >= a and r <= b:
               return self.st[idx]
        UpperCamelCase_							       =       (l + r) // 2
        UpperCamelCase_							       =       self.query_recursive(self.left(__UpperCamelCase     )     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     )
        UpperCamelCase_							       =       self.query_recursive(self.right(__UpperCamelCase     )     ,	mid + 1     ,	__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     )
        return max(__UpperCamelCase     ,	__UpperCamelCase     )

 def lowerCamelCase_				(      self     ):




        """simple docstring"""


        UpperCamelCase_							       =       []
        for i in range(1     ,	N + 1     ):
               show_list += [self.query(__UpperCamelCase     ,	__UpperCamelCase     )]
        print(__UpperCamelCase     )


if __name__ == "__main__":
      _A	  =					[1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
      _A	  =					15
      _A	  =					SegmentTree(A)
      print(segt.query(4, 6))
      print(segt.query(7, 11))
      print(segt.query(7, 12))
      segt.update(1, 3, 111)
      print(segt.query(1, 15))
      segt.update(7, 8, 235)
      segt.show_data()





import warnings
from typing import List, Optional, Union

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

from .configuration_utils import ConfigMixin, register_to_config
from .utils import CONFIG_NAME, PIL_INTERPOLATION, deprecate

class 		lowercase_       (       __SCREAMING_SNAKE_CASE				):
 A__						:				List[str]         =    CONFIG_NAME

 @register_to_config
 def __init__(      self     ,	__UpperCamelCase = True     ,	__UpperCamelCase = 8     ,	__UpperCamelCase = "lanczos"     ,	__UpperCamelCase = True     ,	__UpperCamelCase = False     ,	):




        """simple docstring"""


        super().__init__()

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        if images.ndim == 3:
               UpperCamelCase_							       =       images[None, ...]
        UpperCamelCase_							       =       (images * 2_5_5).round().astype("""uint8"""     )
        if images.shape[-1] == 1:
               # special case for grayscale (single channel) images
               UpperCamelCase_							       =       [Image.fromarray(image.squeeze()     ,	mode="""L"""     ) for image in images]
        else:
               UpperCamelCase_							       =       [Image.fromarray(__UpperCamelCase     ) for image in images]

        return pil_images

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        if not isinstance(__UpperCamelCase     ,	__UpperCamelCase     ):
               UpperCamelCase_							       =       [images]
        UpperCamelCase_							       =       [np.array(__UpperCamelCase     ).astype(np.floataa     ) / 255.0 for image in images]
        UpperCamelCase_							       =       np.stack(__UpperCamelCase     ,	axis=0     )

        return images

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        if images.ndim == 3:
               UpperCamelCase_							       =       images[..., None]

        UpperCamelCase_							       =       torch.from_numpy(images.transpose(0     ,	3     ,	1     ,	2     )     )
        return images

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        UpperCamelCase_							       =       images.cpu().permute(0     ,	2     ,	3     ,	1     ).float().numpy()
        return images

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        return 2.0 * images - 1.0

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        return (images / 2 + 0.5).clamp(0     ,	1     )

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        UpperCamelCase_							       =       image.convert("""RGB"""     )
        return image

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase = None     ,	__UpperCamelCase = None     ,	):




        """simple docstring"""


        if height is None:
               UpperCamelCase_							       =       image.height
        if width is None:
               UpperCamelCase_							       =       image.width

        UpperCamelCase_       ,				UpperCamelCase_							       =       (
            x - x % self.config.vae_scale_factor for x in (width, height)
        )  # resize to integer multiple of vae_scale_factor
        UpperCamelCase_							       =       image.resize((width, height)     ,	resample=PIL_INTERPOLATION[self.config.resample]     )
        return image

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase = None     ,	__UpperCamelCase = None     ,	):




        """simple docstring"""


        UpperCamelCase_							       =       (PIL.Image.Image, np.ndarray, torch.Tensor)
        if isinstance(__UpperCamelCase     ,	__UpperCamelCase     ):
               UpperCamelCase_							       =       [image]
        elif not (isinstance(__UpperCamelCase     ,	__UpperCamelCase     ) and all(isinstance(__UpperCamelCase     ,	__UpperCamelCase     ) for i in image     )):
               raise ValueError(
                   f'''Input is in incorrect format: {[type(__UpperCamelCase     ) for i in image]}. Currently, we only support {", ".join(__UpperCamelCase     )}'''     )

        if isinstance(image[0]     ,	PIL.Image.Image     ):
               if self.config.do_convert_rgb:
                      UpperCamelCase_							       =       [self.convert_to_rgb(__UpperCamelCase     ) for i in image]
               if self.config.do_resize:
                      UpperCamelCase_							       =       [self.resize(__UpperCamelCase     ,	__UpperCamelCase     ,	__UpperCamelCase     ) for i in image]
               UpperCamelCase_							       =       self.pil_to_numpy(__UpperCamelCase     )  # to np
               UpperCamelCase_							       =       self.numpy_to_pt(__UpperCamelCase     )  # to pt

        elif isinstance(image[0]     ,	np.ndarray     ):
               UpperCamelCase_							       =       np.concatenate(__UpperCamelCase     ,	axis=0     ) if image[0].ndim == 4 else np.stack(__UpperCamelCase     ,	axis=0     )
               UpperCamelCase_							       =       self.numpy_to_pt(__UpperCamelCase     )
               UpperCamelCase_       ,				UpperCamelCase_       ,				UpperCamelCase_       ,				UpperCamelCase_							       =       image.shape
               if self.config.do_resize and (
                   height % self.config.vae_scale_factor != 0 or width % self.config.vae_scale_factor != 0
               ):
                      raise ValueError(
                          f'''Currently we only support resizing for PIL image - please resize your numpy array to be divisible by {self.config.vae_scale_factor}'''
                          f'''currently the sizes are {height} and {width}. You can also pass a PIL image instead to use resize option in VAEImageProcessor'''     )

        elif isinstance(image[0]     ,	torch.Tensor     ):
               UpperCamelCase_							       =       torch.cat(__UpperCamelCase     ,	axis=0     ) if image[0].ndim == 4 else torch.stack(__UpperCamelCase     ,	axis=0     )
               UpperCamelCase_       ,				UpperCamelCase_       ,				UpperCamelCase_       ,				UpperCamelCase_							       =       image.shape

               # don't need any preprocess if the image is latents
               if channel == 4:
                      return image

               if self.config.do_resize and (
                   height % self.config.vae_scale_factor != 0 or width % self.config.vae_scale_factor != 0
               ):
                      raise ValueError(
                          f'''Currently we only support resizing for PIL image - please resize your pytorch tensor to be divisible by {self.config.vae_scale_factor}'''
                          f'''currently the sizes are {height} and {width}. You can also pass a PIL image instead to use resize option in VAEImageProcessor'''     )

        # expected range [0,1], normalize to [-1,1]
        UpperCamelCase_							       =       self.config.do_normalize
        if image.min() < 0:
               warnings.warn(
                   """Passing `image` as torch tensor with value range in [-1,1] is deprecated. The expected value range for image tensor is [0,1] """
                   f'''when passing as pytorch tensor or numpy Array. You passed `image` with value range [{image.min()},{image.max()}]'''     ,	__UpperCamelCase     ,	)
               UpperCamelCase_							       =       False

        if do_normalize:
               UpperCamelCase_							       =       self.normalize(__UpperCamelCase     )

        return image

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase = "pil"     ,	__UpperCamelCase = None     ,	):




        """simple docstring"""


        if not isinstance(__UpperCamelCase     ,	torch.Tensor     ):
               raise ValueError(
                   f'''Input for postprocessing is in incorrect format: {type(__UpperCamelCase     )}. We only support pytorch tensor'''     )
        if output_type not in ["latent", "pt", "np", "pil"]:
               UpperCamelCase_							       =       (
                   f'''the output_type {output_type} is outdated and has been set to `np`. Please make sure to set it to one of these instead: '''
                   """`pil`, `np`, `pt`, `latent`"""
               )
               deprecate("""Unsupported output_type"""     ,	"""1.0.0"""     ,	__UpperCamelCase     ,	standard_warn=__UpperCamelCase     )
               UpperCamelCase_							       =       """np"""

        if output_type == "latent":
               return image

        if do_denormalize is None:
               UpperCamelCase_							       =       [self.config.do_normalize] * image.shape[0]

        UpperCamelCase_							       =       torch.stack(
            [self.denormalize(image[i]     ) if do_denormalize[i] else image[i] for i in range(image.shape[0]     )]     )

        if output_type == "pt":
               return image

        UpperCamelCase_							       =       self.pt_to_numpy(__UpperCamelCase     )

        if output_type == "np":
               return image

        if output_type == "pil":
               return self.numpy_to_pil(__UpperCamelCase     )



class 		lowercase_       (       __SCREAMING_SNAKE_CASE				):
 A__						:				List[Any]         =    CONFIG_NAME

 @register_to_config
 def __init__(      self     ,	__UpperCamelCase = True     ,	__UpperCamelCase = 8     ,	__UpperCamelCase = "lanczos"     ,	__UpperCamelCase = True     ,	):




        """simple docstring"""


        super().__init__()

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        if images.ndim == 3:
               UpperCamelCase_							       =       images[None, ...]
        UpperCamelCase_							       =       (images * 2_5_5).round().astype("""uint8"""     )
        if images.shape[-1] == 1:
               # special case for grayscale (single channel) images
               UpperCamelCase_							       =       [Image.fromarray(image.squeeze()     ,	mode="""L"""     ) for image in images]
        else:
               UpperCamelCase_							       =       [Image.fromarray(image[:, :, :3]     ) for image in images]

        return pil_images

 @staticmethod
 def lowerCamelCase_				(      __UpperCamelCase     ):




        """simple docstring"""


        return image[:, :, 1] * 2**8 + image[:, :, 2]

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ):




        """simple docstring"""


        if images.ndim == 3:
               UpperCamelCase_							       =       images[None, ...]
        UpperCamelCase_							       =       images[:, :, :, 3:]
        if images.shape[-1] == 6:
               UpperCamelCase_							       =       (images_depth * 2_5_5).round().astype("""uint8"""     )
               UpperCamelCase_							       =       [
                   Image.fromarray(self.rgblike_to_depthmap(__UpperCamelCase     )     ,	mode="""I;16"""     ) for image_depth in images_depth
               ]
        elif images.shape[-1] == 4:
               UpperCamelCase_							       =       (images_depth * 65_535.0).astype(np.uintaa     )
               UpperCamelCase_							       =       [Image.fromarray(__UpperCamelCase     ,	mode="""I;16"""     ) for image_depth in images_depth]
        else:
               raise Exception("""Not supported"""     )

        return pil_images

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ,	__UpperCamelCase = "pil"     ,	__UpperCamelCase = None     ,	):




        """simple docstring"""


        if not isinstance(__UpperCamelCase     ,	torch.Tensor     ):
               raise ValueError(
                   f'''Input for postprocessing is in incorrect format: {type(__UpperCamelCase     )}. We only support pytorch tensor'''     )
        if output_type not in ["latent", "pt", "np", "pil"]:
               UpperCamelCase_							       =       (
                   f'''the output_type {output_type} is outdated and has been set to `np`. Please make sure to set it to one of these instead: '''
                   """`pil`, `np`, `pt`, `latent`"""
               )
               deprecate("""Unsupported output_type"""     ,	"""1.0.0"""     ,	__UpperCamelCase     ,	standard_warn=__UpperCamelCase     )
               UpperCamelCase_							       =       """np"""

        if do_denormalize is None:
               UpperCamelCase_							       =       [self.config.do_normalize] * image.shape[0]

        UpperCamelCase_							       =       torch.stack(
            [self.denormalize(image[i]     ) if do_denormalize[i] else image[i] for i in range(image.shape[0]     )]     )

        UpperCamelCase_							       =       self.pt_to_numpy(__UpperCamelCase     )

        if output_type == "np":
               if image.shape[-1] == 6:
                      UpperCamelCase_							       =       np.stack([self.rgblike_to_depthmap(im[:, :, 3:]     ) for im in image]     ,	axis=0     )
               else:
                      UpperCamelCase_							       =       image[:, :, :, 3:]
               return image[:, :, :, :3], image_depth

        if output_type == "pil":
               return self.numpy_to_pil(__UpperCamelCase     ), self.numpy_to_depth(__UpperCamelCase     )
        else:
               raise Exception(f'''This type {output_type} is not supported'''     )



