





import random

class 					__A   :


				def __init__(						self      ,       UpperCAmelCase_      ,       UpperCAmelCase_							):
								lowerCamelCase		       =x
								lowerCamelCase		       =y


				def _snake_case				(						self							):
								return (self.x**2 + self.y**2) <= 1


				@classmethod
				def _snake_case				(						cls							):
								return cls(x=random.random()      ,       y=random.random()							)





def    _lowercase    (  _UpperCAmelCase )  ->     float:
				if number_of_simulations < 1:
								raise ValueError("""At least one simulation is necessary to estimate PI.""" )

				lowerCamelCase		       =0
				for _ in range(_UpperCAmelCase ):
								lowerCamelCase		       =Point.random_unit_square()

								if random_point.is_in_unit_circle():
												number_in_unit_circle += 1

				return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
							# import doctest

							# doctest.testmod()
							from math import pi

							UpperCAmelCase__  :	Dict     ='''Please enter the desired number of Monte Carlo simulations: '''
							UpperCAmelCase__  :	str     =estimate_pi(int(input(prompt).strip()))
							print(F"An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}")











import unittest
from dataclasses import dataclass
from typing import Optional

from transformers.utils import ModelOutput
@dataclass
class       __a					( __lowerCamelCase     ):


     """simple docstring"""


     _A				:    float
     _A				:    Optional[float]									=  None
     _A				:    Optional[float]									=  None






class       __a					( unittest.TestCase     ):


     """simple docstring"""


     def   __A				(	self			: Dict						)		->   Optional[int]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         self.assertEqual(x.a				,3_0						)
         self.assertIsNone(x.b						)
         self.assertIsNone(x.c						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.d




     def   __A				(	self			: Tuple						)		->   Dict:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,b=1_0						)
         self.assertEqual(x[0]				,3_0						)
         self.assertEqual(x[1]				,1_0						)
         self.assertEqual(x[:2]				,(3_0, 1_0)						)
         self.assertEqual(x[:]				,(3_0, 1_0)						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,c=1_0						)
         self.assertEqual(x[0]				,3_0						)
         self.assertEqual(x[1]				,1_0						)
         self.assertEqual(x[:2]				,(3_0, 1_0)						)
         self.assertEqual(x[:]				,(3_0, 1_0)						)




     def   __A				(	self			: List[str]						)		->   Dict:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,b=1_0						)
         self.assertEqual(x["""a"""]				,3_0						)
         self.assertEqual(x["""b"""]				,1_0						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x["""c"""]

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,c=1_0						)
         self.assertEqual(x["""a"""]				,3_0						)
         self.assertEqual(x["""c"""]				,1_0						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x["""b"""]




     def   __A				(	self			: Optional[int]						)		->   List[str]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         self.assertEqual(list(x.keys()						)				,["""a"""]						)
         self.assertEqual(list(x.values()						)				,[3_0]						)
         self.assertEqual(list(x.items()						)				,[("""a""", 3_0)]						)
         self.assertEqual(list(_UpperCamelCase						)				,["""a"""]						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,b=1_0						)
         self.assertEqual(list(x.keys()						)				,["""a""", """b"""]						)
         self.assertEqual(list(x.values()						)				,[3_0, 1_0]						)
         self.assertEqual(list(x.items()						)				,[("""a""", 3_0), ("""b""", 1_0)]						)
         self.assertEqual(list(_UpperCamelCase						)				,["""a""", """b"""]						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,c=1_0						)
         self.assertEqual(list(x.keys()						)				,["""a""", """c"""]						)
         self.assertEqual(list(x.values()						)				,[3_0, 1_0]						)
         self.assertEqual(list(x.items()						)				,[("""a""", 3_0), ("""c""", 1_0)]						)
         self.assertEqual(list(_UpperCamelCase						)				,["""a""", """c"""]						)

         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.update({"""d""": 2_0}						)
         with self.assertRaises(_UpperCamelCase						):
             del x["a"]
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.pop("""a"""						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.setdefault("""d"""				,3_2						)




     def   __A				(	self			: int						)		->   List[Any]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         SCREAMING_SNAKE_CASE__								=1_0
         self.assertEqual(x.a				,1_0						)
         self.assertEqual(x["""a"""]				,1_0						)




     def   __A				(	self			: Union[str, Any]						)		->   Optional[Any]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         SCREAMING_SNAKE_CASE__								=1_0
         self.assertEqual(x.a				,1_0						)
         self.assertEqual(x["""a"""]				,1_0						)




     def   __A				(	self			: Dict						)		->   List[str]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest({"""a""": 3_0, """b""": 1_0}						)
         self.assertEqual(list(x.keys()						)				,["""a""", """b"""]						)
         self.assertEqual(x.a				,3_0						)
         self.assertEqual(x.b				,1_0						)




     def   __A				(	self			: Optional[int]						)		->   int:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest([("""a""", 3_0), ("""b""", 1_0)]						)
         self.assertEqual(list(x.keys()						)				,["""a""", """b"""]						)
         self.assertEqual(x.a				,3_0						)
         self.assertEqual(x.b				,1_0						)

         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=ModelOutputTest([("""a""", 3_0), (1_0, 1_0)]						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=(3_0, 3_0)						)
         self.assertEqual(list(x.keys()						)				,["""a"""]						)
         self.assertEqual(x.a				,(3_0, 3_0)						)






