




from __future__ import annotations

from fractions import Fraction




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase ):
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=[]
				__magic_name__						:						List[Any]										=11
				__magic_name__						:						Tuple										=int("""1""" + """0""" * digit_len )
				for num in range(lowerCamelCase						,  lowerCamelCase ):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(lowerCamelCase						,  lowerCamelCase ):
																				solutions.append(F"{num}/{den}" )
												den += 1
								num += 1
								__magic_name__						:						List[str]										=10
				return solutions




def 		lowerCAmelCase_ (						lowerCamelCase = 2 ):
				__magic_name__						:						str										=1.0
				for fraction in fraction_list(lowerCamelCase ):
								__magic_name__						:						int										=Fraction(lowerCamelCase )
								result *= frac.denominator / frac.numerator
				return int(lowerCamelCase )


if __name__ == "__main__":
							print(solution())





'''simple docstring'''

import gc
import threading
import time

import psutil
import torch


class     __UpperCAmelCase       :





  def __init__(	self ):
     lowerCAmelCase_			=      psutil.Process()
     lowerCAmelCase_			=      False





  def 						UpperCAmelCase_	(	self ):
     lowerCAmelCase_			=      -1

     while True:
        lowerCAmelCase_			=      max(self.process.memory_info().rss    ,     self.cpu_memory_peak )

        # can't sleep or will not catch the peak right (this comment is here on purpose)
        if not self.peak_monitoring:
           break





  def 						UpperCAmelCase_	(	self ):
     lowerCAmelCase_			=      True
     lowerCAmelCase_			=      threading.Thread(target=self.peak_monitor )
     lowerCAmelCase_			=      True
     self.thread.start()







  def 						UpperCAmelCase_	(	self ):
     lowerCAmelCase_			=      False
     self.thread.join()
     return self.cpu_memory_peak






A_     :						List[str]    							=PeakCPUMemory()



def snake_case_      (					)			->					Tuple:
   # Time
   lowerCAmelCase_			=      {'''time''': time.time()}

   gc.collect()
   torch.cuda.empty_cache()

   # CPU mem
   lowerCAmelCase_			=      psutil.Process().memory_info().rss
   cpu_peak_tracker.start()

   # GPU mem
   for i in range(torch.cuda.device_count()):
      lowerCAmelCase_			=      torch.cuda.memory_allocated(__snake_case)
   torch.cuda.reset_peak_memory_stats()

   return measures



def snake_case_      (					__snake_case  :							Any)			->					List[str]:
   # Time
   lowerCAmelCase_			=      {'''time''': time.time() - start_measures['''time''']}

   gc.collect()
   torch.cuda.empty_cache()

   # CPU mem
   lowerCAmelCase_			=      (psutil.Process().memory_info().rss - start_measures['''cpu''']) / 2**20
   lowerCAmelCase_			=      (cpu_peak_tracker.stop() - start_measures['''cpu''']) / 2**20

   # GPU mem
   for i in range(torch.cuda.device_count()):
      lowerCAmelCase_			=      (torch.cuda.memory_allocated(__snake_case) - start_measures[str(__snake_case)]) / 2**20
      lowerCAmelCase_			=      (torch.cuda.max_memory_allocated(__snake_case) - start_measures[str(__snake_case)]) / 2**20

   return measures






def snake_case_      (					__snake_case  :							Dict	,   __snake_case  :							Optional[int])			->					Dict:
   print(F'''{description}:''')
   print(F'''- Time: {measures['time']:.2f}s''')
   for i in range(torch.cuda.device_count()):
      print(F'''- GPU {i} allocated: {measures[str(__snake_case)]:.2f}MiB''')
      lowerCAmelCase_			=      measures[F'''{i}-peak''']
      print(F'''- GPU {i} peak: {peak:.2f}MiB''')
   print(F'''- CPU RAM allocated: {measures['cpu']:.2f}MiB''')
   print(F'''- CPU RAM peak: {measures['cpu-peak']:.2f}MiB''')





