'''simple docstring'''




import os
from itertools import chain
from random import randrange, shuffle

import pytest

from .sola import PokerHand

_A								=   (
    '''4S 3H 2C 7S 5H''',
    '''9D 8H 2C 6S 7H''',
    '''2D 6D 9D TH 7D''',
    '''TC 8C 2S JH 6C''',
    '''JH 8S TH AH QH''',
    '''TS KS 5S 9S AC''',
    '''KD 6S 9D TH AD''',
    '''KS 8D 4D 9S 4S''',  # pair
    '''8C 4S KH JS 4D''',  # pair
    '''QH 8H KD JH 8S''',  # pair
    '''KC 4H KS 2H 8D''',  # pair
    '''KD 4S KC 3H 8S''',  # pair
    '''AH 8S AS KC JH''',  # pair
    '''3H 4C 4H 3S 2H''',  # 2 pairs
    '''5S 5D 2C KH KH''',  # 2 pairs
    '''3C KH 5D 5S KH''',  # 2 pairs
    '''AS 3C KH AD KH''',  # 2 pairs
    '''7C 7S 3S 7H 5S''',  # 3 of a kind
    '''7C 7S KH 2H 7H''',  # 3 of a kind
    '''AC KH QH AH AS''',  # 3 of a kind
    '''2H 4D 3C AS 5S''',  # straight (low ace)
    '''3C 5C 4C 2C 6H''',  # straight
    '''6S 8S 7S 5H 9H''',  # straight
    '''JS QS 9H TS KH''',  # straight
    '''QC KH TS JS AH''',  # straight (high ace)
    '''8C 9C 5C 3C TC''',  # flush
    '''3S 8S 9S 5S KS''',  # flush
    '''4C 5C 9C 8C KC''',  # flush
    '''JH 8H AH KH QH''',  # flush
    '''3D 2H 3H 2C 2D''',  # full house
    '''2H 2C 3S 3H 3D''',  # full house
    '''KH KC 3S 3H 3D''',  # full house
    '''JC 6H JS JD JH''',  # 4 of a kind
    '''JC 7H JS JD JH''',  # 4 of a kind
    '''JC KH JS JD JH''',  # 4 of a kind
    '''2S AS 4S 5S 3S''',  # straight flush (low ace)
    '''2D 6D 3D 4D 5D''',  # straight flush
    '''5C 6C 3C 7C 4C''',  # straight flush
    '''JH 9H TH KH QH''',  # straight flush
    '''JH AH TH KH QH''',  # royal flush (high ace straight flush)
)

_A								=   (
    ('''2H 3H 4H 5H 6H''', '''KS AS TS QS JS''', '''Loss'''),
    ('''2H 3H 4H 5H 6H''', '''AS AD AC AH JD''', '''Win'''),
    ('''AS AH 2H AD AC''', '''JS JD JC JH 3D''', '''Win'''),
    ('''2S AH 2H AS AC''', '''JS JD JC JH AD''', '''Loss'''),
    ('''2S AH 2H AS AC''', '''2H 3H 5H 6H 7H''', '''Win'''),
    ('''AS 3S 4S 8S 2S''', '''2H 3H 5H 6H 7H''', '''Win'''),
    ('''2H 3H 5H 6H 7H''', '''2S 3H 4H 5S 6C''', '''Win'''),
    ('''2S 3H 4H 5S 6C''', '''3D 4C 5H 6H 2S''', '''Tie'''),
    ('''2S 3H 4H 5S 6C''', '''AH AC 5H 6H AS''', '''Win'''),
    ('''2S 2H 4H 5S 4C''', '''AH AC 5H 6H AS''', '''Loss'''),
    ('''2S 2H 4H 5S 4C''', '''AH AC 5H 6H 7S''', '''Win'''),
    ('''6S AD 7H 4S AS''', '''AH AC 5H 6H 7S''', '''Loss'''),
    ('''2S AH 4H 5S KC''', '''AH AC 5H 6H 7S''', '''Loss'''),
    ('''2S 3H 6H 7S 9C''', '''7H 3C TH 6H 9S''', '''Loss'''),
    ('''4S 5H 6H TS AC''', '''3S 5H 6H TS AC''', '''Win'''),
    ('''2S AH 4H 5S 6C''', '''AD 4C 5H 6H 2C''', '''Tie'''),
    ('''AS AH 3H AD AC''', '''AS AH 2H AD AC''', '''Win'''),
    ('''AH AC 5H 5C QS''', '''AH AC 5H 5C KS''', '''Loss'''),
    ('''AH AC 5H 5C QS''', '''KH KC 5H 5C QS''', '''Win'''),
    ('''7C 7S KH 2H 7H''', '''3C 3S AH 2H 3H''', '''Win'''),
    ('''3C 3S AH 2H 3H''', '''7C 7S KH 2H 7H''', '''Loss'''),
    ('''6H 5H 4H 3H 2H''', '''5H 4H 3H 2H AH''', '''Win'''),
    ('''5H 4H 3H 2H AH''', '''5H 4H 3H 2H AH''', '''Tie'''),
    ('''5H 4H 3H 2H AH''', '''6H 5H 4H 3H 2H''', '''Loss'''),
    ('''AH AD KS KC AC''', '''AH KD KH AC KC''', '''Win'''),
    ('''2H 4D 3C AS 5S''', '''2H 4D 3C 6S 5S''', '''Loss'''),
    ('''2H 3S 3C 3H 2S''', '''3S 3C 2S 2H 2D''', '''Win'''),
    ('''4D 6D 5D 2D JH''', '''3S 8S 3H TC KH''', '''Loss'''),
    ('''4S 6C 8S 3S 7S''', '''AD KS 2D 7D 7C''', '''Loss'''),
    ('''6S 4C 7H 8C 3H''', '''5H JC AH 9D 9C''', '''Loss'''),
    ('''9D 9H JH TC QH''', '''3C 2S JS 5C 7H''', '''Win'''),
    ('''2H TC 8S AD 9S''', '''4H TS 7H 2C 5C''', '''Win'''),
    ('''9D 3S 2C 7S 7C''', '''JC TD 3C TC 9H''', '''Loss'''),
)

_A								=   (
    ('''2H 3H 4H 5H 6H''', True),
    ('''AS AH 2H AD AC''', False),
    ('''2H 3H 5H 6H 7H''', True),
    ('''KS AS TS QS JS''', True),
    ('''8H 9H QS JS TH''', False),
    ('''AS 3S 4S 8S 2S''', True),
)

_A								=   (
    ('''2H 3H 4H 5H 6H''', True),
    ('''AS AH 2H AD AC''', False),
    ('''2H 3H 5H 6H 7H''', False),
    ('''KS AS TS QS JS''', True),
    ('''8H 9H QS JS TH''', True),
)

_A								=   (
    ('''2H 4D 3C AS 5S''', True, [5, 4, 3, 2, 1_4]),
    ('''2H 5D 3C AS 5S''', False, [1_4, 5, 5, 3, 2]),
    ('''JH QD KC AS TS''', False, [1_4, 1_3, 1_2, 1_1, 1_0]),
    ('''9D 3S 2C 7S 7C''', False, [9, 7, 7, 3, 2]),
)

_A								=   (
    ('''JH AH TH KH QH''', 0),
    ('''JH 9H TH KH QH''', 0),
    ('''JC KH JS JD JH''', 7),
    ('''KH KC 3S 3H 3D''', 6),
    ('''8C 9C 5C 3C TC''', 0),
    ('''JS QS 9H TS KH''', 0),
    ('''7C 7S KH 2H 7H''', 3),
    ('''3C KH 5D 5S KH''', 2),
    ('''QH 8H KD JH 8S''', 1),
    ('''2D 6D 9D TH 7D''', 0),
)

_A								=   (
    ('''JH AH TH KH QH''', 2_3),
    ('''JH 9H TH KH QH''', 2_2),
    ('''JC KH JS JD JH''', 2_1),
    ('''KH KC 3S 3H 3D''', 2_0),
    ('''8C 9C 5C 3C TC''', 1_9),
    ('''JS QS 9H TS KH''', 1_8),
    ('''7C 7S KH 2H 7H''', 1_7),
    ('''3C KH 5D 5S KH''', 1_6),
    ('''QH 8H KD JH 8S''', 1_5),
    ('''2D 6D 9D TH 7D''', 1_4),
)

def _UpperCamelCase   (       ):
     lowercase_					:       Optional[Any]     				=					randrange(len(_lowercase							)							), randrange(len(_lowercase							)							)
     lowercase_					:       List[Any]     				=					['Loss', 'Tie', 'Win'][(play >= oppo) + (play > oppo)]
     lowercase_					:       str     				=					SORTED_HANDS[play], SORTED_HANDS[oppo]
     return hand, other, expected

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_ = 100							):
     return (generate_random_hand() for _ in range(_lowercase							))

@pytest.mark.parametrize('hand, expected'  ,       _lowercase							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     assert PokerHand(_lowercase							)._is_flush() == expected

@pytest.mark.parametrize('hand, expected'  ,       _lowercase							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     assert PokerHand(_lowercase							)._is_straight() == expected

@pytest.mark.parametrize('hand, expected, card_values'  ,       _lowercase							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     lowercase_					:       List[Any]     				=					PokerHand(_lowercase							)
     assert player._is_five_high_straight() == expected
     assert player._card_values == card_values

@pytest.mark.parametrize('hand, expected'  ,       _lowercase							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     assert PokerHand(_lowercase							)._is_same_kind() == expected

@pytest.mark.parametrize('hand, expected'  ,       _lowercase							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     assert PokerHand(_lowercase							)._hand_type == expected

@pytest.mark.parametrize('hand, other, expected'  ,       _lowercase							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     assert PokerHand(_lowercase							).compare_with(PokerHand(_lowercase							)							) == expected

@pytest.mark.parametrize('hand, other, expected'  ,       generate_random_hands()							)
def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     assert PokerHand(_lowercase							).compare_with(PokerHand(_lowercase							)							) == expected

def _UpperCamelCase   (       ):
     lowercase_					:       Optional[int]     				=					[PokerHand(_lowercase							) for hand in SORTED_HANDS]
     lowercase_					:       Tuple     				=					poker_hands.copy()
     shuffle(_lowercase							)
     lowercase_					:       Optional[int]     				=					chain(sorted(_lowercase							)							)
     for index, hand in enumerate(_lowercase							):
          assert hand == poker_hands[index]

def _UpperCamelCase   (       ):
     # Test that five high straights are compared correctly.
     lowercase_					:       List[Any]     				=					[PokerHand('2D AC 3H 4H 5S'							), PokerHand('2S 3H 4H 5S 6C'							)]
     pokerhands.sort(reverse=_lowercase							)
     assert pokerhands[0].__str__() == "2S 3H 4H 5S 6C"

def _UpperCamelCase   (       ):
     # Multiple calls to five_high_straight function should still return True
     # and shouldn't mutate the list in every call other than the first.
     lowercase_					:       Tuple     				=					PokerHand('2C 4S AS 3D 5C'							)
     lowercase_					:       Any     				=					True
     lowercase_					:       Optional[Any]     				=					[5, 4, 3, 2, 14]
     for _ in range(10							):
          assert pokerhand._is_five_high_straight() == expected
          assert pokerhand._card_values == expected_card_values






def _UpperCamelCase   (       ):
     # Problem number 54 from Project Euler
     # Testing from poker_hands.txt file
     lowercase_					:       Optional[int]     				=					0
     lowercase_					:       int     				=					os.path.abspath(os.path.dirname(_lowercase							)							)
     lowercase_					:       Optional[int]     				=					os.path.join(_lowercase  ,       'poker_hands.txt'							)
     with open(_lowercase							) as file_hand:
          for line in file_hand:
               lowercase_					:       Optional[int]     				=					line[:14].strip()
               lowercase_					:       str     				=					line[15:].strip()
               lowercase_					:       str     				=					PokerHand(_lowercase							), PokerHand(_lowercase							)
               lowercase_					:       Optional[int]     				=					player.compare_with(_lowercase							)
               if output == "Win":
                    answer += 1
     assert answer == 376







'''simple docstring'''




from decimal import Decimal, getcontext
from math import ceil, factorial

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):

     if not isinstance(SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
          raise TypeError('Undefined for non-integers'							)
     elif precision < 1:
          raise ValueError('Undefined for non-natural numbers'							)

     lowercase_					:       str     				=					precision
     lowercase_					:       List[str]     				=					ceil(precision / 14							)
     lowercase_					:       Union[str, Any]     				=					426_880 * Decimal(10_005							).sqrt()
     lowercase_					:       List[Any]     				=					1
     lowercase_					:       Optional[int]     				=					13_591_409
     lowercase_					:       Dict     				=					Decimal(SCREAMING_SNAKE_CASE_							)
     for k in range(1  ,       SCREAMING_SNAKE_CASE_							):
          lowercase_					:       List[str]     				=					factorial(6 * k							) // (factorial(3 * k							) * factorial(SCREAMING_SNAKE_CASE_							) ** 3)
          linear_term += 545_140_134
          exponential_term *= -262_537_412_640_768_000
          partial_sum += Decimal(multinomial_term * linear_term							) / exponential_term
     return str(constant_term / partial_sum							)[:-1]


if __name__ == "__main__":
 _A								=   5_0
 print(F"""The first {n} digits of pi is: {pi(n)}""")




