


import functools
import gc
import inspect

import torch

from .imports import is_npu_available, is_xpu_available

def 						_UpperCAmelCase				(			*SCREAMING_SNAKE_CASE__			:					Union[str, Any]				):
     if not isinstance(SCREAMING_SNAKE_CASE__			,     SCREAMING_SNAKE_CASE__				):
          __UpperCamelCase    							=list(SCREAMING_SNAKE_CASE__				)
     for i in range(len(SCREAMING_SNAKE_CASE__				)				):
          __UpperCamelCase    							=None
     gc.collect()
     if is_xpu_available():
          torch.xpu.empty_cache()
     elif is_npu_available():
          torch.npu.empty_cache()
     else:
          torch.cuda.empty_cache()
     return objects

def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					Exception				):
     __UpperCamelCase    							=[
         'CUDA out of memory.',  # CUDA OOM
         'cuDNN error: CUDNN_STATUS_NOT_SUPPORTED.',  # CUDNN SNAFU
         'DefaultCPUAllocator: can\'t allocate memory',  # CPU OOM
     ]
     if isinstance(SCREAMING_SNAKE_CASE__			,     SCREAMING_SNAKE_CASE__				) and len(exception.args				) == 1:
          return any(err in exception.args[0] for err in _statements				)
     return False





def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					callable = None			,     SCREAMING_SNAKE_CASE__			:					int = 1_28				):
     if function is None:
          return functools.partial(SCREAMING_SNAKE_CASE__			,     starting_batch_size=SCREAMING_SNAKE_CASE__				)

     __UpperCamelCase    							=starting_batch_size

     def decorator(*SCREAMING_SNAKE_CASE__			:					Union[str, Any]			,     **SCREAMING_SNAKE_CASE__			:					Optional[Any]				):
          nonlocal batch_size
          gc.collect()
          if is_xpu_available():
               torch.xpu.empty_cache()
          elif is_npu_available():
               torch.npu.empty_cache()
          else:
               torch.cuda.empty_cache()
          __UpperCamelCase    							=list(inspect.signature(SCREAMING_SNAKE_CASE__				).parameters.keys()				)
          # Guard against user error
          if len(SCREAMING_SNAKE_CASE__				) < (len(SCREAMING_SNAKE_CASE__				) + 1):
               __UpperCamelCase    							=', '.join([F'{arg}={value}' for arg, value in zip(params[1:]			,     args[1:]				)]				)
               raise TypeError(
                   F'Batch size was passed into `{function.__name__}` as the first argument when called.'
                   F'Remove this as the decorator already does so: `{function.__name__}({arg_str})`'				)
          while True:
               if batch_size == 0:
                    raise RuntimeError('No executable batch size found, reached zero.'				)
               try:
                    return function(SCREAMING_SNAKE_CASE__			,     *SCREAMING_SNAKE_CASE__			,     **SCREAMING_SNAKE_CASE__				)
               except Exception as e:
                    if should_reduce_batch_size(SCREAMING_SNAKE_CASE__				):
                         gc.collect()
                         if is_xpu_available():
                              torch.xpu.empty_cache()
                         elif is_npu_available():
                              torch.npu.empty_cache()
                         else:
                              torch.cuda.empty_cache()
                         batch_size //= 2
                    else:
                         raise

     return decorator









from __future__ import annotations

import math






class     UpperCAmelCase__       :



    """simple docstring"""






    def __init__(			self					,   A_    )  ->       None:
         __UpperCamelCase    							=size
         # approximate the overall size of segment tree with given value
         __UpperCamelCase    							=[0 for i in range(0					,   4 * size    )]
         # create array to store lazy update
         __UpperCamelCase    							=[0 for i in range(0					,   4 * size    )]
         __UpperCamelCase    							=[0 for i in range(0					,   4 * size    )]  # flag for lazy update






    def _a					(			self					,   A_    )  ->       int:
         return idx * 2






    def _a					(			self					,   A_    )  ->       int:
         return idx * 2 + 1






    def _a					(			self					,   A_					,   A_					,   A_					,   A_    )  ->       None:
         if left_element == right_element:
              __UpperCamelCase    							=a[left_element - 1]
         else:
              __UpperCamelCase    							=(left_element + right_element) // 2
              self.build(self.left(A_    )					,   A_					,   A_					,   A_    )
              self.build(self.right(A_    )					,   mid + 1					,   A_					,   A_    )
              __UpperCamelCase    							=max(
                  self.segment_tree[self.left(A_    )]					,   self.segment_tree[self.right(A_    )]    )






    def _a					(			self					,   A_					,   A_					,   A_					,   A_					,   A_					,   A_    )  ->       bool:
         if self.flag[idx] is True:
              __UpperCamelCase    							=self.lazy[idx]
              __UpperCamelCase    							=False
              if left_element != right_element:
                   __UpperCamelCase    							=self.lazy[idx]
                   __UpperCamelCase    							=self.lazy[idx]
                   __UpperCamelCase    							=True
                   __UpperCamelCase    							=True

         if right_element < a or left_element > b:
              return True
         if left_element >= a and right_element <= b:
              __UpperCamelCase    							=val
              if left_element != right_element:
                   __UpperCamelCase    							=val
                   __UpperCamelCase    							=val
                   __UpperCamelCase    							=True
                   __UpperCamelCase    							=True
              return True
         __UpperCamelCase    							=(left_element + right_element) // 2
         self.update(self.left(A_    )					,   A_					,   A_					,   A_					,   A_					,   A_    )
         self.update(self.right(A_    )					,   mid + 1					,   A_					,   A_					,   A_					,   A_    )
         __UpperCamelCase    							=max(
             self.segment_tree[self.left(A_    )]					,   self.segment_tree[self.right(A_    )]    )
         return True






    def _a					(			self					,   A_					,   A_					,   A_					,   A_					,   A_    )  ->       int | float:
         if self.flag[idx] is True:
              __UpperCamelCase    							=self.lazy[idx]
              __UpperCamelCase    							=False
              if left_element != right_element:
                   __UpperCamelCase    							=self.lazy[idx]
                   __UpperCamelCase    							=self.lazy[idx]
                   __UpperCamelCase    							=True
                   __UpperCamelCase    							=True
         if right_element < a or left_element > b:
              return -math.inf
         if left_element >= a and right_element <= b:
              return self.segment_tree[idx]
         __UpperCamelCase    							=(left_element + right_element) // 2
         __UpperCamelCase    							=self.query(self.left(A_    )					,   A_					,   A_					,   A_					,   A_    )
         __UpperCamelCase    							=self.query(self.right(A_    )					,   mid + 1					,   A_					,   A_					,   A_    )
         return max(A_					,   A_    )






    def __str__(			self    )  ->       str:
         return str([self.query(1					,   1					,   self.size					,   A_					,   A_    ) for i in range(1					,   self.size + 1    )]    )


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





