





"""simple docstring"""





from typing import List

import numpy as np


def       lowerCamelCase_       (   UpperCAmelCase_  )						->int:





  """simple docstring"""


  __UpperCAmelCase    :						Tuple       =						{key: len(UpperCAmelCase_  ) for key, value in gen_kwargs.items() if isinstance(UpperCAmelCase_  ,			UpperCAmelCase_  )}
  if len(set(lists_lengths.values()  )  ) > 1:
    raise RuntimeError(
        (
            '''Sharding is ambiguous for this dataset: '''
            + '''we found several data sources lists of different lengths, and we don\'t know over which list we should parallelize:\n'''
            + '''\n'''.join(f'''\t- key {key} has length {length}''' for key, length in lists_lengths.items()  )
            + '''\nTo fix this, check the \'gen_kwargs\' and make sure to use lists only for data sources, '''
            + '''and use tuples otherwise. In the end there should only be one single list, or several lists with the same length.'''
        )  )
  __UpperCAmelCase    :						Any       =						max(lists_lengths.values()  ,			default=0  )
  return max(1  ,			UpperCAmelCase_  )


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->List[range]:





  """simple docstring"""


  __UpperCAmelCase    :						Dict       =						[]
  for group_idx in range(UpperCAmelCase_  ):
    __UpperCAmelCase    :						Dict       =						num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
    if num_shards_to_add == 0:
      break
    __UpperCAmelCase    :						str       =						shards_indices_per_group[-1].stop if shards_indices_per_group else 0
    __UpperCAmelCase    :						str       =						range(UpperCAmelCase_  ,			start + num_shards_to_add  )
    shards_indices_per_group.append(UpperCAmelCase_  )
  return shards_indices_per_group


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->List[dict]:





  """simple docstring"""


  __UpperCAmelCase    :						str       =						_number_of_shards_in_gen_kwargs(UpperCAmelCase_  )
  if num_shards == 1:
    return [dict(UpperCAmelCase_  )]
  else:
    __UpperCAmelCase    :						int       =						_distribute_shards(num_shards=UpperCAmelCase_  ,			max_num_jobs=UpperCAmelCase_  )
    return [
        {
            key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
            if isinstance(UpperCAmelCase_  ,			UpperCAmelCase_  )
            else value
            for key, value in gen_kwargs.items()
        }
        for group_idx in range(len(UpperCAmelCase_  )  )
    ]


def       lowerCamelCase_       (   UpperCAmelCase_  )						->dict:





  """simple docstring"""


  return {
      key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
      if isinstance(gen_kwargs_list[0][key]  ,			UpperCAmelCase_  )
      else gen_kwargs_list[0][key]
      for key in gen_kwargs_list[0]
  }







def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->dict:





  """simple docstring"""


  __UpperCAmelCase    :						Union[str, Any]       =						{len(UpperCAmelCase_  ) for value in gen_kwargs.values() if isinstance(UpperCAmelCase_  ,			UpperCAmelCase_  )}
  __UpperCAmelCase    :						Dict       =						{}
  for size in list_sizes:
    __UpperCAmelCase    :						Dict       =						list(range(UpperCAmelCase_  )  )
    rng.shuffle(indices_per_size[size]  )
  # Now let's copy the gen_kwargs and shuffle the lists based on their sizes
  __UpperCAmelCase    :						int       =						dict(UpperCAmelCase_  )
  for key, value in shuffled_kwargs.items():
    if isinstance(UpperCAmelCase_  ,			UpperCAmelCase_  ):
      __UpperCAmelCase    :						Optional[Any]       =						[value[i] for i in indices_per_size[len(UpperCAmelCase_  )]]
  return shuffled_kwargs






"""simple docstring"""





from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

lowercase__				:int				   =       TypeVar('T')




class 							snake_case							(			Generic[T] ):

      '''simple docstring'''



      def __init__(							self       :      Optional[Any]						,				__lowercase       :      list[T]						,				__lowercase       :      Callable[[T, T], T] ):


        '''simple docstring'''




        __UpperCAmelCase    :						Any | T       =						None

        __UpperCAmelCase    :						int       =						len(__lowercase )
        __UpperCAmelCase    :						list[T]       =						[any_type for _ in range(self.N )] + arr
        __UpperCAmelCase    :						List[Any]       =						fnc
        self.build()

      def       A_					(							self       :      str ):


        '''simple docstring'''




        for p in range(self.N - 1						,				0						,				-1 ):
          __UpperCAmelCase    :						Any       =						self.fn(self.st[p * 2]						,				self.st[p * 2 + 1] )

      def       A_					(							self       :      Union[str, Any]						,				__lowercase       :      int						,				__lowercase       :      T ):


        '''simple docstring'''




        p += self.N
        __UpperCAmelCase    :						Tuple       =						v
        while p > 1:
          __UpperCAmelCase    :						Union[str, Any]       =						p // 2
          __UpperCAmelCase    :						Any       =						self.fn(self.st[p * 2]						,				self.st[p * 2 + 1] )







      def       A_					(							self       :      str						,				__lowercase       :      int						,				__lowercase       :      int ):  # noqa: E741


        '''simple docstring'''




        __UpperCAmelCase       ,     __UpperCAmelCase    :						int       =						l + self.N, r + self.N

        __UpperCAmelCase    :						T | None       =						None
        while l <= r:
          if l % 2 == 1:
            __UpperCAmelCase    :						Any       =						self.st[l] if res is None else self.fn(__lowercase						,				self.st[l] )
          if r % 2 == 0:
            __UpperCAmelCase    :						Any       =						self.st[r] if res is None else self.fn(__lowercase						,				self.st[r] )
          __UpperCAmelCase       ,     __UpperCAmelCase    :						Any       =						(l + 1) // 2, (r - 1) // 2
        return res


if __name__ == "__main__":
  from functools import reduce

  lowercase__				:Any				   =       [1, 1_0, -2, 9, -3, 8, 4, -7, 5, 6, 1_1, -1_2]

  lowercase__				:List[Any]				   =       {
      0: 7,
      1: 2,
      2: 6,
      3: -1_4,
      4: 5,
      5: 4,
      6: 7,
      7: -1_0,
      8: 9,
      9: 1_0,
      1_0: 1_2,
      1_1: 1,
  }

  lowercase__				:List[str]				   =       SegmentTree(test_array, min)
  lowercase__				:List[str]				   =       SegmentTree(test_array, max)
  lowercase__				:Tuple				   =       SegmentTree(test_array, lambda a, b: a + b)


  def       lowerCamelCase_       (   )						->None:





    """simple docstring"""


    for i in range(len(UpperCAmelCase_  )  ):
      for j in range(UpperCAmelCase_  ,			len(UpperCAmelCase_  )  ):
        __UpperCAmelCase    :						Optional[Any]       =						reduce(UpperCAmelCase_  ,			test_array[i : j + 1]  )
        __UpperCAmelCase    :						Optional[int]       =						reduce(UpperCAmelCase_  ,			test_array[i : j + 1]  )
        __UpperCAmelCase    :						Union[str, Any]       =						reduce(lambda UpperCAmelCase_  ,			UpperCAmelCase_  : a + b  ,			test_array[i : j + 1]  )
        assert min_range == min_segment_tree.query(UpperCAmelCase_  ,			UpperCAmelCase_  )
        assert max_range == max_segment_tree.query(UpperCAmelCase_  ,			UpperCAmelCase_  )
        assert sum_range == sum_segment_tree.query(UpperCAmelCase_  ,			UpperCAmelCase_  )

  test_all_segments()

  for index, value in test_updates.items():
    lowercase__				:Optional[Any]				   =       value
    min_segment_tree.update(index, value)
    max_segment_tree.update(index, value)
    sum_segment_tree.update(index, value)
    test_all_segments()