




'''simple docstring'''

import importlib.metadata
import operator
import re
import sys
from typing import Optional

from packaging import version


a  :				Dict									=  {
    '<': operator.lt,
    '<=': operator.le,
    '==': operator.eq,
    '!=': operator.ne,
    '>=': operator.ge,
    '>': operator.gt,
}


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase	)		->					int:

					'''simple docstring'''

					if got_ver is None or want_ver is None:
										raise ValueError(
										    F"Unable to compare versions for {requirement}: need={want_ver} found={got_ver}. This is unusual. Consider"
										    F" reinstalling {pkg}."	)
					if not ops[op](version.parse(__UpperCAmelCase	),      version.parse(__UpperCAmelCase	)	):
										raise ImportError(
										    F"{requirement} is required for a normal functioning of this module, but found {pkg}=={got_ver}.{hint}"	)


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase = None	)		->					None:

					'''simple docstring'''

					snake_case_									=				F"\n{hint}" if hint is not None else ''''''

					# non-versioned check
					if re.match(r'''^[\w_\-\d]+$''',      __UpperCAmelCase	):
										snake_case_			,snake_case_			,snake_case_									=				requirement, None, None
					else:
										snake_case_									=				re.findall(r'''^([^!=<>\s]+)([\s!=<>]{1,2}.+)''',      __UpperCAmelCase	)
										if not match:
															raise ValueError(
															    '''requirement needs to be in the pip package format, .e.g., package_a==1.23, or package_b>=1.23, but'''
															    F" got {requirement}"	)
										snake_case_			,snake_case_									=				match[0]
										snake_case_									=				want_full.split(''','''	)  # there could be multiple requirements
										snake_case_									=				{}
										for w in want_range:
															snake_case_									=				re.findall(r'''^([\s!=<>]{1,2})(.+)''',      __UpperCAmelCase	)
															if not match:
																				raise ValueError(
																				    '''requirement needs to be in the pip package format, .e.g., package_a==1.23, or package_b>=1.23,'''
																				    F" but got {requirement}"	)
															snake_case_			,snake_case_									=				match[0]
															snake_case_									=				want_ver
															if op not in ops:
																				raise ValueError(F"{requirement}: need one of {list(ops.keys()	)}, but got {op}"	)

    # special case
					if pkg == "python":
										snake_case_									=				'''.'''.join([str(__UpperCAmelCase	) for x in sys.version_info[:3]]	)
										for op, want_ver in wanted.items():
															_compare_versions(__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase	)
										return

					# check if any version is installed
					try:
										snake_case_									=				importlib.metadata.version(__UpperCAmelCase	)
					except importlib.metadata.PackageNotFoundError:
										raise importlib.metadata.PackageNotFoundError(
										    F"The '{requirement}' distribution was not found and is required by this application. {hint}"	)

					# check that the right version is installed if version number or a range was provided
					if want_ver is not None:
										for op, want_ver in wanted.items():
															_compare_versions(__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase	)


def 		__magic_name__    (	__UpperCAmelCase	)		->					Dict:

					'''simple docstring'''

					snake_case_									=				'''Try: pip install transformers -U or pip install -e \'.[dev]\' if you\'re working with git main'''
					return require_version(__UpperCAmelCase,      __UpperCAmelCase	)





"""simple docstring"""







from __future__ import annotations

from functools import lru_cache
from math import ceil

lowerCAmelCase__      				=   100

lowerCAmelCase__      				=   set(range(3, NUM_PRIMES, 2))
primes.add(2)
lowerCAmelCase__      				=   42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
     if prime not in primes:
          continue
     primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))
@lru_cache(maxsize=1_0_0				)
def 					a__			(				SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  if number_to_partition < 0:
    return set()
  elif number_to_partition == 0:
    return {1}

  lowerCAmelCase     :     set[int]								=							set()
  lowerCAmelCase     :     int
  lowerCAmelCase     :     int

  for prime in primes:
    if prime > number_to_partition:
      continue
    for sub in partition(number_to_partition - prime				):
      ret.add(sub * prime				)

  return ret
def 					a__			(				SCREAMING_SNAKE_CASE    :    int = 5_0_0_0				):


  '''simple docstring'''







  for number_to_partition in range(1				,      SCREAMING_SNAKE_CASE				):
    if len(partition(SCREAMING_SNAKE_CASE				)				) > number_unique_partitions:
      return number_to_partition
  return None


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





