





import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
lowerCAmelCase							:       int					 =	object()

# For specifying empty leaf dict `{}`
lowerCAmelCase							:       Optional[int]					 =	object()






def 		lowerCAmelCase  (	UpperCamelCase__   :   Union[str, Any]       ,			UpperCamelCase__   :   Any					)      ->    List[Any]:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				Optional[Any]           =   tuple((re.compile(x + '''$'''					) for x in qs)					)
						for i in range(len(UpperCamelCase__					) - len(UpperCamelCase__					) + 1					):
												__SCREAMING_SNAKE_CASE:				str           =   [x.match(UpperCamelCase__					) for x, y in zip(UpperCamelCase__       ,			ks[i:]					)]
												if matches and all(UpperCamelCase__					):
																		return True
						return False






def 		lowerCAmelCase  (	UpperCamelCase__   :   Tuple					)      ->    int:

						"""simple docstring"""





						def replace(UpperCamelCase__   :   Optional[int]       ,			UpperCamelCase__   :   Any					):
												for rule, replacement in rules:
																		if _match(UpperCamelCase__       ,			UpperCamelCase__					):
																								return replacement
												return val

						return replace






def 		lowerCAmelCase  (	)      ->    str:

						"""simple docstring"""





						return [
						    # embeddings
						    (("transformer", "wpe", "embedding"), P('''mp'''       ,			UpperCamelCase__					)),
						    (("transformer", "wte", "embedding"), P('''mp'''       ,			UpperCamelCase__					)),
						    # atention
						    (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(UpperCamelCase__       ,			'''mp'''					)),
						    (("attention", "out_proj", "kernel"), P('''mp'''       ,			UpperCamelCase__					)),
						    (("attention", "out_proj", "bias"), None),
						    # mlp
						    (("mlp", "c_fc", "kernel"), P(UpperCamelCase__       ,			'''mp'''					)),
						    (("mlp", "c_fc", "bias"), P('''mp'''					)),
						    (("mlp", "c_proj", "kernel"), P('''mp'''       ,			UpperCamelCase__					)),
						    (("mlp", "c_proj", "bias"), None),
						    # layer norms
						    ((r"ln_\d+", "bias"), None),
						    ((r"\d+", r"ln_\d+", "scale"), None),
						    (("ln_f", "bias"), None),
						    (("ln_f", "scale"), None),
						]






def 		lowerCAmelCase  (	UpperCamelCase__   :   str					)      ->    Tuple:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				Optional[Any]           =   _get_partition_rules()
						__SCREAMING_SNAKE_CASE:				Dict           =   _replacement_rules(UpperCamelCase__					)
						__SCREAMING_SNAKE_CASE:				Optional[Any]           =   {k: _unmatched for k in flatten_dict(UpperCamelCase__					)}
						__SCREAMING_SNAKE_CASE:				Dict           =   {k: replace(UpperCamelCase__       ,			UpperCamelCase__					) for k, v in initd.items()}
						assert _unmatched not in result.values(), "Incomplete partition spec."
						return freeze(unflatten_dict(UpperCamelCase__					)					)










def 		lowerCAmelCase  (	UpperCamelCase__   :   List[Any]       ,			UpperCamelCase__   :   Dict					)      ->    List[Any]:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				int           =   [0 for i in range(r + 1					)]
						# nc0 = 1
						__SCREAMING_SNAKE_CASE:				Dict           =   1
						for i in range(1       ,			n + 1					):
												# to compute current row from previous row.
												__SCREAMING_SNAKE_CASE:				Optional[Any]           =   min(UpperCamelCase__       ,			UpperCamelCase__					)
												while j > 0:
																		c[j] += c[j - 1]
																		j -= 1
						return c[r]




print(binomial_coefficient(n=10, r=5))



