

'''simple docstring'''





from itertools import product

def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					int = 15    ):



     '''simple docstring'''





     lowercase__					:     float   = 0.0
     lowercase__					:     float
     lowercase__					:     int
     lowercase__					:     int
     lowercase__					:     int
     lowercase__					:     int
     lowercase__					:     tuple[int, ...]

     for series in product(range(2    )			,  repeat=SCREAMING_SNAKE_CASE_    ):
          lowercase__					:     Union[str, Any]   = series.count(1    )
          lowercase__					:     List[str]   = num_turns - num_blue
          if num_red >= num_blue:
               continue
          lowercase__					:     str   = 1.0
          for ind, col in enumerate(SCREAMING_SNAKE_CASE_			,  2    ):
               if col == 0:
                    prob *= (ind - 1) / ind
               else:
                    prob *= 1 / ind

          total_prob += prob

     return int(1 / total_prob    )


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




# as due to their complexity multi-gpu tests could impact other tests, and to aid debug we have those in a separate module.

import os
import sys

from transformers.testing_utils import TestCasePlus, execute_subprocess_async, get_gpu_count, require_torch_gpu, slow

from .utils import load_json


class    SCREAMING_SNAKE_CASE__      (__snake_case  ):





    @classmethod
    def    snake_case_       (   cls):
         return cls





    @slow
    @require_torch_gpu
    def    snake_case_       (   self):
         lowercase__					:     List[Any]   = self.get_auto_remove_tmp_dir()
         lowercase__					:     List[str]   = f"""
            --model_name Helsinki-NLP/opus-mt-en-ro
            --save_dir {output_dir}
            --data_dir {self.test_file_dir_str}/test_data/wmt_en_ro
            --num_beams 2
            --task translation
        """.split()

         # we want this test to run even if there is only one GPU, but if there are more we use them all
         lowercase__					:     int   = get_gpu_count()
         lowercase__					:     Tuple   = f"""
            -m torch.distributed.launch
            --nproc_per_node={n_gpu}
            {self.test_file_dir}/run_distributed_eval.py
        """.split()
         lowercase__					:     Optional[Any]   = [sys.executable] + distributed_args + args
         execute_subprocess_async(a		,     env=self.get_env())

         lowercase__					:     str   = os.path.join(a		,     'test_bleu.json')
         lowercase__					:     List[str]   = load_json(a)
         # print(metrics)
         self.assertGreaterEqual(metrics['bleu']		,     25)

