





from __future__ import annotations


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		int):



		'''simple docstring'''






		__lowerCAmelCase			=				[0] * max_one

		for i in range(0     ,							__lowercase):
				__lowerCAmelCase			=				i

		for i in range(2     ,							__lowercase):
				if totients[i] == i:
						for j in range(__lowercase     ,							__lowercase     ,							__lowercase):
								totients[j] -= totients[j] // i

		return totients


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		int     ,							__lowercase:		int):



		'''simple docstring'''






		return sorted(str(__lowercase)) == sorted(str(__lowercase))


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		int = 10_00_00_00):



		'''simple docstring'''






		__lowerCAmelCase			=				1  # i
		__lowerCAmelCase			=				0  # φ(i)
		__lowerCAmelCase			=				get_totients(max_n + 1)

		for i in range(2     ,							max_n + 1):
				__lowerCAmelCase			=				totients[i]

				if i * min_denominator < min_numerator * t and has_same_digits(__lowercase     ,							__lowercase):
						__lowerCAmelCase			=				i
						__lowerCAmelCase			=				t

		return min_numerator


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







import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_multi_gpu,
    require_single_gpu,
    test_sync,
)
from accelerate.utils import patch_environment

class   __snake_case				(			unittest.TestCase   ):






    '''simple docstring'''





    def 	A		(   self						:		int							):

      """simple docstring"""





      __lowerCAmelCase			=				inspect.getfile(accelerate.test_utils							)
      __lowerCAmelCase			=				os.path.sep.join(mod_file.split(os.path.sep							)[:-1] + ['''scripts''', '''test_sync.py''']							)





    @require_cpu
    def 	A		(   self						:		str							):

      """simple docstring"""





      debug_launcher(test_sync.main			,						num_processes=1							)





    @require_cpu
    def 	A		(   self						:		List[str]							):

      """simple docstring"""





      debug_launcher(test_sync.main							)





    @require_single_gpu
    def 	A		(   self						:		Optional[Any]							):

      """simple docstring"""





      test_sync.main()





    @require_multi_gpu
    def 	A		(   self						:		Union[str, Any]							):

      """simple docstring"""





      print(f'''Found {torch.cuda.device_count()} devices.'''							)
      __lowerCAmelCase			=				['''torchrun''', f'''--nproc_per_node={torch.cuda.device_count()}''', self.test_file_path]
      with patch_environment(omp_num_threads=1							):
        execute_subprocess_async(snake_case			,						env=os.environ.copy()							)
