


"""simple docstring"""







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 _A		(		lowercase	):







    """simple docstring"""
    a					={node: {node} for node in graph}

    a					={node: graph[node][:] for node in graph}

    while len(lowercase	) > 2:
        # Choose a random edge.
        a					=random.choice(list(graph_copy.keys()	)	)
        a					=random.choice(graph_copy[u]	)

        # Contract edge (u, v) to new node uv
        a					=u + v
        a					=list(set(graph_copy[u] + graph_copy[v]	)	)
        uv_neighbors.remove(lowercase	)
        uv_neighbors.remove(lowercase	)
        a					=uv_neighbors
        for neighbor in uv_neighbors:
            graph_copy[neighbor].append(lowercase	)

        a					=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(lowercase	)
            if v in graph_copy[neighbor]:
                graph_copy[neighbor].remove(lowercase	)

    # Find cutset.
    a					=[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))



"""simple docstring"""







from math import gcd
def _A		(		lowercase = 1_20_00	):







    """simple docstring"""
    a					=0
    for d in range(max_d + 1	):
        for n in range(d // 3 + 1 ,					(d + 1) // 2	):
            if gcd(lowercase ,					lowercase	) == 1:
                fractions_number += 1
    return fractions_number


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