import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


lowerCAmelCase			:							int     ="\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n"


lowerCAmelCase			:							Union[str, Any]     ="\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.\n"


lowerCAmelCase			:							Optional[int]     =r"\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")\n\nExamples:\n    >>> metric = datasets.load_metric(\"competition_math\")\n    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])\n    >>> print(results)\n    {'accuracy': 1.0}\n"




@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION ,  _KWARGS_DESCRIPTION		)
class 	__snake_case	( datasets.Metric		):





      '''simple docstring'''






      def 	_SCREAMING_SNAKE_CASE    (					self     :				Dict)				->Any:


          """simple docstring"""


          return datasets.MetricInfo(
              description=_DESCRIPTION    ,  citation=_CITATION    ,  inputs_description=_KWARGS_DESCRIPTION    ,  features=datasets.Features(
                  {
                      """predictions""": datasets.Value("""string"""),
                      """references""": datasets.Value("""string"""),
                  })    ,  homepage="""https://github.com/hendrycks/math"""    ,  codebase_urls=["""https://github.com/hendrycks/math"""]    ,  )




      def 	_SCREAMING_SNAKE_CASE    (					self     :				List[Any]    ,  _UpperCamelCase     :				Any    ,  _UpperCamelCase     :				str)				->Any:


          """simple docstring"""


          _lowerCamelCase     :		Any 						=						0.0
          for i, j in zip(_UpperCamelCase    ,  _UpperCamelCase):
              n_correct += 1.0 if math_equivalence.is_equiv(_UpperCamelCase    ,  _UpperCamelCase) else 0.0
          _lowerCamelCase     :		str 						=						n_correct / len(_UpperCamelCase)
          return {
              "accuracy": accuracy,
          }





from __future__ import annotations

lowerCAmelCase			:							int     =[]







def 						A__  (					__A   , __A   , __A	):







    '''simple docstring'''
    for i in range(len(__A	)	):
        if board[row][i] == 1:
            return False
    for i in range(len(__A	)	):
        if board[i][column] == 1:
            return False
    for i, j in zip(range(__A   , -1   , -1	)   , range(__A   , -1   , -1	)	):
        if board[i][j] == 1:
            return False
    for i, j in zip(range(__A   , -1   , -1	)   , range(__A   , len(__A	)	)	):
        if board[i][j] == 1:
            return False
    return True







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    if row >= len(__A	):
        solution.append(__A	)
        printboard(__A	)
        print()
        return True
    for i in range(len(__A	)	):
        if is_safe(__A   , __A   , __A	):
            _lowerCamelCase     :		int 						=						1
            solve(__A   , row + 1	)
            _lowerCamelCase     :		List[str] 						=						0
    return False







def 						A__  (					__A	):







    '''simple docstring'''
    for i in range(len(__A	)	):
        for j in range(len(__A	)	):
            if board[i][j] == 1:
                print("""Q"""   , end=""" """	)
            else:
                print("""."""   , end=""" """	)
        print()


# n=int(input("The no. of queens"))
lowerCAmelCase			:							int     =8
lowerCAmelCase			:							Union[str, Any]     =[[0 for i in range(n)] for j in range(n)]
solve(board, 0)
print("The total no. of solutions are :", len(solution))




