code: def tree_width(N, to_binary=False):
      """Generate tree width suitable for ``merge_sorted`` given N inputs
  
      The larger N is, the more tasks are reduced in a single task.
  
      In theory, this is designed so all tasks are of comparable effort.
      """
      if N < 32:
          group_size = 2
      else:
          group_size = int(math.log(N))
      num_groups = N // group_size
      if to_binary or num_groups < 16:
          return 2 ** int(math.log(N / group_size, 2))
      else:
          return num_groups
  
imports: from __future__ import annotations
  import math
  import numpy
  import pandas
  from pandas.api.types import is_datetime64_dtype, is_integer_dtype
  from tlz import merge, merge_sorted, take
  from dask.base import tokenize
  from dask.dataframe.core import Series
  from dask.dataframe.dispatch import tolist_dispatch
  from dask.utils import is_cupy_type, random_state_data
label_desc: Use image node_id 2 for calling a global function with example usage: tree_width(N, to_binary) and returns: unknown, num_groups