






"""simple docstring"""






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



def 					_A			(__a    ,				__a    ,				__a    ,				__a							) ->       Any:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_      :  Dict    						=		sum(a_i[j] for j in range(__a    ,				len(__a							)							)							)
    SCREAMING_SNAKE_CASE_      :  Optional[int]    						=		sum(a_i[j] * base[j] for j in range(min(len(__a							)    ,				__a							)							)							)

    SCREAMING_SNAKE_CASE_						,			SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		0, 0
    SCREAMING_SNAKE_CASE_      :  str    						=		n - i

    SCREAMING_SNAKE_CASE_      :  Dict    						=		memo.get(__a							)

    if sub_memo is not None:
        SCREAMING_SNAKE_CASE_      :  str    						=		sub_memo.get(__a							)

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

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

        else:
            SCREAMING_SNAKE_CASE_      :  Optional[Any]    						=		[]
    else:
        SCREAMING_SNAKE_CASE_      :  List[Any]    						=		{c: []}
        SCREAMING_SNAKE_CASE_      :  Optional[int]    						=		sub_memo

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

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

    SCREAMING_SNAKE_CASE_      :  List[str]    						=		sub_memo[c]

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

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



def 					_A			(__a    ,				__a    ,				__a    ,				__a							) ->       Optional[int]:
    """simple docstring"""






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

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

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

            ds_c += a_i[j]

        if addend > 0:
            break

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



def 					_A			(__a    ,				__a    ,				__a							) ->       Optional[Any]:
    """simple docstring"""






    for j in range(__a    ,				len(__a							)							):
        SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		digits[j] + addend
        if s >= 10:
            SCREAMING_SNAKE_CASE_						,			SCREAMING_SNAKE_CASE_      :  Optional[Any]    						=		divmod(__a    ,				10							)
            SCREAMING_SNAKE_CASE_      :  Optional[int]    						=		addend // 10 + quotient
        else:
            SCREAMING_SNAKE_CASE_      :  Tuple    						=		s
            SCREAMING_SNAKE_CASE_      :  Tuple    						=		addend // 10

        if addend == 0:
            break

    while addend > 0:
        SCREAMING_SNAKE_CASE_						,			SCREAMING_SNAKE_CASE_      :  str    						=		divmod(__a    ,				10							)
        digits.append(__a							)



def 					_A			(__a = 10**15							) ->       int:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_      :  Optional[int]    						=		[1]
    SCREAMING_SNAKE_CASE_      :  Dict    						=		1
    SCREAMING_SNAKE_CASE_      :  Dict    						=		0
    while True:
        SCREAMING_SNAKE_CASE_						,			SCREAMING_SNAKE_CASE_      :  List[Any]    						=		next_term(__a    ,				20    ,				i + dn    ,				__a							)
        dn += terms_jumped
        if dn == n - i:
            break

    SCREAMING_SNAKE_CASE_      :  List[str]    						=		0
    for j in range(len(__a							)							):
        a_n += digits[j] * 10**j
    return a_n


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









from sklearn.metrics import fa_score

import datasets


__lowerCamelCase       :     List[Any]   =     """
The F1 score is the harmonic mean of the precision and recall. It can be computed with the equation:
F1 = 2 * (precision * recall) / (precision + recall)
"""


__lowerCamelCase       :     List[Any]   =     """
Args:
    predictions (`list` of `int`): Predicted labels.
    references (`list` of `int`): Ground truth labels.
    labels (`list` of `int`): The set of labels to include when `average` is not set to `'binary'`, and the order of the labels if `average` is `None`. Labels present in the data can be excluded, for example to calculate a multiclass average ignoring a majority negative class. Labels not present in the data will result in 0 components in a macro average. For multilabel targets, labels are column indices. By default, all labels in `predictions` and `references` are used in sorted order. Defaults to None.
    pos_label (`int`): The class to be considered the positive class, in the case where `average` is set to `binary`. Defaults to 1.
    average (`string`): This parameter is required for multiclass/multilabel targets. If set to `None`, the scores for each class are returned. Otherwise, this determines the type of averaging performed on the data. Defaults to `'binary'`.

        - 'binary': Only report results for the class specified by `pos_label`. This is applicable only if the classes found in `predictions` and `references` are binary.
        - 'micro': Calculate metrics globally by counting the total true positives, false negatives and false positives.
        - 'macro': Calculate metrics for each label, and find their unweighted mean. This does not take label imbalance into account.
        - 'weighted': Calculate metrics for each label, and find their average weighted by support (the number of true instances for each label). This alters `'macro'` to account for label imbalance. This option can result in an F-score that is not between precision and recall.
        - 'samples': Calculate metrics for each instance, and find their average (only meaningful for multilabel classification).
    sample_weight (`list` of `float`): Sample weights Defaults to None.

Returns:
    f1 (`float` or `array` of `float`): F1 score or list of f1 scores, depending on the value passed to `average`. Minimum possible value is 0. Maximum possible value is 1. Higher f1 scores are better.

Examples:

    Example 1-A simple binary example
        >>> f1_metric = datasets.load_metric(\"f1\")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0])
        >>> print(results)
        {'f1': 0.5}

    Example 2-The same simple binary example as in Example 1, but with `pos_label` set to `0`.
        >>> f1_metric = datasets.load_metric(\"f1\")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], pos_label=0)
        >>> print(round(results['f1'], 2))
        0.67

    Example 3-The same simple binary example as in Example 1, but with `sample_weight` included.
        >>> f1_metric = datasets.load_metric(\"f1\")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], sample_weight=[0.9, 0.5, 3.9, 1.2, 0.3])
        >>> print(round(results['f1'], 2))
        0.35

    Example 4-A multiclass example, with different values for the `average` input.
        >>> predictions = [0, 2, 1, 0, 0, 1]
        >>> references = [0, 1, 2, 0, 1, 2]
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=\"macro\")
        >>> print(round(results['f1'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=\"micro\")
        >>> print(round(results['f1'], 2))
        0.33
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=\"weighted\")
        >>> print(round(results['f1'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=None)
        >>> print(results)
        {'f1': array([0.8, 0. , 0. ])}
"""


__lowerCamelCase       :     str   =     """
@article{scikit-learn,
    title={Scikit-learn: Machine Learning in {P}ython},
    author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
           and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
           and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
           Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
    journal={Journal of Machine Learning Research},
    volume={12},
    pages={2825--2830},
    year={2011}
}
"""



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





      def        __UpperCamelCase( self   ):
       '''simple docstring'''




       return datasets.MetricInfo(
           description=_DESCRIPTION       ,							citation=_CITATION       ,							inputs_description=_KWARGS_DESCRIPTION       ,							features=datasets.Features(
               {
                   "predictions": datasets.Sequence(datasets.Value("int32"   )   ),
                   "references": datasets.Sequence(datasets.Value("int32"   )   ),
               }
               if self.config_name == "multilabel"
               else {
                   "predictions": datasets.Value("int32"   ),
                   "references": datasets.Value("int32"   ),
               }   )       ,							reference_urls=["https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html"]       ,							)





      def        __UpperCamelCase( self       ,							A_       ,							A_       ,							A_=None       ,							A_=1       ,							A_="binary"       ,							A_=None   ):
       '''simple docstring'''




       UpperCamelCase	:					List[str]       	=   fa_score(
           A_       ,							A_       ,							labels=A_       ,							pos_label=A_       ,							average=A_       ,							sample_weight=A_   )
       return {"f1": float(A_   ) if score.size == 1 else score}
