




from scipy.stats import spearmanr

import datasets


UpperCAmelCase_		:					Optional[Any]          =  "\nThe Spearman rank-order correlation coefficient is a measure of the\nrelationship between two datasets. Like other correlation coefficients,\nthis one varies between -1 and +1 with 0 implying no correlation.\nPositive correlations imply that as data in dataset x increases, so\ndoes data in dataset y. Negative correlations imply that as x increases,\ny decreases. Correlations of -1 or +1 imply an exact monotonic relationship.\n\nUnlike the Pearson correlation, the Spearman correlation does not\nassume that both datasets are normally distributed.\n\nThe p-value roughly indicates the probability of an uncorrelated system\nproducing datasets that have a Spearman correlation at least as extreme\nas the one computed from these datasets. The p-values are not entirely\nreliable but are probably reasonable for datasets larger than 500 or so.\n"

UpperCAmelCase_		:					Tuple          =  "\nArgs:\n    predictions (`List[float]`): Predicted labels, as returned by a model.\n    references (`List[float]`): Ground truth labels.\n    return_pvalue (`bool`): If `True`, returns the p-value. If `False`, returns\n            only the spearmanr score. Defaults to `False`.\nReturns:\n    spearmanr (`float`): Spearman correlation coefficient.\n    p-value (`float`): p-value. **Note**: is only returned if `return_pvalue=True` is input.\nExamples:\n    Example 1:\n        >>> spearmanr_metric = datasets.load_metric(\"spearmanr\")\n        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4])\n        >>> print(results)\n        {'spearmanr': -0.7}\n\n    Example 2:\n        >>> spearmanr_metric = datasets.load_metric(\"spearmanr\")\n        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5],\n        ...                                     predictions=[10, 9, 2.5, 6, 4],\n        ...                                     return_pvalue=True)\n        >>> print(results['spearmanr'])\n        -0.7\n        >>> print(round(results['spearmanr_pvalue'], 2))\n        0.19\n"

UpperCAmelCase_		:					List[Any]          =  R"\\n@book{kokoska2000crc,\n  title={CRC standard probability and statistics tables and formulae},\n  author={Kokoska, Stephen and Zwillinger, Daniel},\n  year={2000},\n  publisher={Crc Press}\n}\n@article{2020SciPy-NMeth,\n  author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and\n            Haberland, Matt and Reddy, Tyler and Cournapeau, David and\n            Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and\n            Bright, Jonathan and {van der Walt}, St{\'e}fan J. and\n            Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and\n            Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and\n            Kern, Robert and Larson, Eric and Carey, C J and\n            Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and\n            {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and\n            Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and\n            Harris, Charles R. and Archibald, Anne M. and\n            Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and\n            {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},\n  title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific\n            Computing in Python}},\n  journal = {Nature Methods},\n  year    = {2020},\n  volume  = {17},\n  pages   = {261--272},\n  adsurl  = {https://rdcu.be/b08Wh},\n  doi     = {10.1038/s41592-019-0686-2},\n}\n"




@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION       ,    _KWARGS_DESCRIPTION      )
class 		__A   (      datasets.Metric      ):

						def      A__    (		self :Optional[Any]			):
										'''simple docstring'''

										return datasets.MetricInfo(
										    description=_DESCRIPTION     ,			citation=_CITATION     ,			inputs_description=_KWARGS_DESCRIPTION     ,			features=datasets.Features(
										        {
										            """predictions""": datasets.Value("""float"""			),
										            """references""": datasets.Value("""float"""			),
										        }			)     ,			reference_urls=["""https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html"""]     ,			)


						def      A__    (		self :Union[str, Any]     ,			__snake_case :str     ,			__snake_case :Optional[int]     ,			__snake_case :str=False			):
										'''simple docstring'''

										__magic_name__						:						Any										=spearmanr(__snake_case     ,			__snake_case			)
										if return_pvalue:
														return {"spearmanr": results[0], "spearmanr_pvalue": results[1]}
										else:
														return {"spearmanr": results[0]}










UpperCAmelCase_		:					int          =  range(2, 20 + 1)
UpperCAmelCase_		:					Tuple          =  [10**k for k in range(ks[-1] + 1)]
UpperCAmelCase_		:					dict[int, dict[int, list[list[int]]]]          =  {}




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				__magic_name__						:						Union[str, Any]										=sum(a_i[j] for j in range(lowerCamelCase						,  len(lowerCamelCase ) ) )
				__magic_name__						:						Any										=sum(a_i[j] * base[j] for j in range(min(len(lowerCamelCase )						,  lowerCamelCase ) ) )

				__magic_name__					,			__magic_name__						:						Tuple										=0, 0
				__magic_name__						:						Optional[Any]										=n - i

				__magic_name__						:						Union[str, Any]										=memo.get(lowerCamelCase )

				if sub_memo is not None:
								__magic_name__						:						int										=sub_memo.get(lowerCamelCase )

								if jumps is not None and len(lowerCamelCase ) > 0:
												# find and make the largest jump without going over
												__magic_name__						:						Dict										=-1
												for _k in range(len(lowerCamelCase ) - 1						,  -1						,  -1 ):
																if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																				__magic_name__						:						Optional[Any]										=_k
																				break

												if max_jump >= 0:
																__magic_name__					,			__magic_name__					,			__magic_name__						:						Optional[int]										=jumps[max_jump]
																# since the difference between jumps is cached, add c
																__magic_name__						:						Tuple										=diff + c
																for j in range(min(lowerCamelCase						,  len(lowerCamelCase ) ) ):
																				__magic_name__					,			__magic_name__						:						Tuple										=divmod(lowerCamelCase						,  10 )
																if new_c > 0:
																				add(lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase )

								else:
												__magic_name__						:						str										=[]
				else:
								__magic_name__						:						List[str]										={c: []}
								__magic_name__						:						List[str]										=sub_memo

				if dn >= max_dn or c + diff >= base[k]:
								return diff, dn

				if k > ks[0]:
								while True:
												# keep doing smaller jumps
												__magic_name__					,			__magic_name__						:						Union[str, Any]										=next_term(lowerCamelCase						,  k - 1						,  i + dn						,  lowerCamelCase )
												diff += _diff
												dn += terms_jumped

												if dn >= max_dn or c + diff >= base[k]:
																break
				else:
								# would be too small a jump, just compute sequential terms instead
								__magic_name__					,			__magic_name__						:						Optional[int]										=compute(lowerCamelCase						,  lowerCamelCase						,  i + dn						,  lowerCamelCase )
								diff += _diff
								dn += terms_jumped

				__magic_name__						:						Tuple										=sub_memo[c]

				# keep jumps sorted by # of terms skipped
				__magic_name__						:						List[Any]										=0
				while j < len(lowerCamelCase ):
								if jumps[j][1] > dn:
												break
								j += 1

				# cache the jump for this value digitsum(b) and c
				sub_memo[c].insert(lowerCamelCase						,  (diff, dn, k) )
				return (diff, dn)




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				if i >= n:
								return 0, i
				if k > len(lowerCamelCase ):
								a_i.extend([0 for _ in range(k - len(lowerCamelCase ) )] )

				# note: a_i -> b * 10^k + c
				# ds_b -> digitsum(b)
				# ds_c -> digitsum(c)
				__magic_name__						:						Tuple										=i
				__magic_name__					,			__magic_name__					,			__magic_name__						:						Tuple										=0, 0, 0
				for j in range(len(lowerCamelCase ) ):
								if j >= k:
												ds_b += a_i[j]
								else:
												ds_c += a_i[j]

				while i < n:
								i += 1
								__magic_name__						:						Optional[Any]										=ds_c + ds_b
								diff += addend
								__magic_name__						:						str										=0
								for j in range(lowerCamelCase ):
												__magic_name__						:						int										=a_i[j] + addend
												__magic_name__					,			__magic_name__						:						Any										=divmod(lowerCamelCase						,  10 )

												ds_c += a_i[j]

								if addend > 0:
												break

				if addend > 0:
								add(lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase )
				return diff, i - start_i




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				for j in range(lowerCamelCase						,  len(lowerCamelCase ) ):
								__magic_name__						:						Tuple										=digits[j] + addend
								if s >= 10:
												__magic_name__					,			__magic_name__						:						int										=divmod(lowerCamelCase						,  10 )
												__magic_name__						:						int										=addend // 10 + quotient
								else:
												__magic_name__						:						Dict										=s
												__magic_name__						:						Any										=addend // 10

								if addend == 0:
												break

				while addend > 0:
								__magic_name__					,			__magic_name__						:						Union[str, Any]										=divmod(lowerCamelCase						,  10 )
								digits.append(lowerCamelCase )




def 		lowerCAmelCase_ (						lowerCamelCase = 10**15 ):
				__magic_name__						:						List[str]										=[1]
				__magic_name__						:						str										=1
				__magic_name__						:						str										=0
				while True:
								__magic_name__					,			__magic_name__						:						List[str]										=next_term(lowerCamelCase						,  20						,  i + dn						,  lowerCamelCase )
								dn += terms_jumped
								if dn == n - i:
												break

				__magic_name__						:						int										=0
				for j in range(len(lowerCamelCase ) ):
								a_n += digits[j] * 10**j
				return a_n


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




