def 			UpperCamelCase__						(    A__      ,			A__ = 1000   )       -> str:
				if (not isinstance(A__      ,			A__   )) or (digit_position <= 0):
								raise ValueError('Digit position must be a positive integer'   )
				elif (not isinstance(A__      ,			A__   )) or (precision < 0):
								raise ValueError('Precision must be a nonnegative integer'   )

				# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
				# accurate
				snake_case__ :     Optional[Any] 							=				(
				    4 * _subsum(A__      ,			1      ,			A__   )
				    - 2 * _subsum(A__      ,			4      ,			A__   )
				    - _subsum(A__      ,			5      ,			A__   )
				    - _subsum(A__      ,			6      ,			A__   )
				)

				# return the first hex digit of the fractional part of the result
				return hex(int((sum_result % 1) * 16   )   )[2:]
def 			UpperCamelCase__						(    A__      ,			A__      ,			A__   )       -> float:
				snake_case__ :     List[str] 							=				0.0
				for sum_index in range(digit_pos_to_extract + precision   ):
								snake_case__ :     Union[str, Any] 							=				8 * sum_index + denominator_addend
								if sum_index < digit_pos_to_extract:
												# if the exponential term is an integer and we mod it by the denominator
												# before dividing, only the integer part of the sum will change;
												# the fractional part will not
												snake_case__ :     Union[str, Any] 							=				pow(
												    16      ,			digit_pos_to_extract - 1 - sum_index      ,			A__   )
								else:
												snake_case__ :     int 							=				pow(16      ,			digit_pos_to_extract - 1 - sum_index   )
								total += exponential_term / denominator
				return total


if __name__ == "__main__":
				import doctest

				doctest.testmod()



from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
lowerCAmelCase__					:       Dict		=       {
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}
def 			UpperCamelCase__						(    A__   )       -> set[tuple[str, str]]:
				snake_case__ :     Tuple 							=				{node: {node} for node in graph}

				snake_case__ :     Tuple 							=				{node: graph[node][:] for node in graph}

				while len(A__   ) > 2:
								# Choose a random edge.
								snake_case__ :     Union[str, Any] 							=				random.choice(list(graph_copy.keys()   )   )
								snake_case__ :     Any 							=				random.choice(graph_copy[u]   )

								# Contract edge (u, v) to new node uv
								snake_case__ :     Tuple 							=				u + v
								snake_case__ :     Dict 							=				list(set(graph_copy[u] + graph_copy[v]   )   )
								uv_neighbors.remove(A__   )
								uv_neighbors.remove(A__   )
								snake_case__ :     Optional[Any] 							=				uv_neighbors
								for neighbor in uv_neighbors:
												graph_copy[neighbor].append(A__   )

								snake_case__ :     Tuple 							=				set(contracted_nodes[u].union(contracted_nodes[v]   )   )

								# Remove nodes u and v.
								del graph_copy[u]
								del graph_copy[v]
								for neighbor in uv_neighbors:
												if u in graph_copy[neighbor]:
																graph_copy[neighbor].remove(A__   )
												if v in graph_copy[neighbor]:
																graph_copy[neighbor].remove(A__   )

    # Find cutset.
				snake_case__ :     Tuple 							=				[contracted_nodes[node] for node in graph_copy]
				return {
				    (node, neighbor)
				    for node in groups[0]
				    for neighbor in graph[node]
				    if neighbor in groups[1]
				}


if __name__ == "__main__":
				print(partition_graph(TEST_GRAPH))


