
"""simple docstring"""


def     _lowerCamelCase(__UpperCamelCase = 998001       )				-> int:

	# fetches the next number
	for number in range(n - 1    , 9999    , -1       ):
		_lowerCAmelCase								=str(__UpperCamelCase       )

		# checks whether 'str_number' is a palindrome.
		if str_number == str_number[::-1]:
			_lowerCAmelCase								=999

			# if 'number' is a product of two 3-digit numbers
			# then number is the answer otherwise fetch next number.
			while divisor != 99:
				if (number % divisor == 0) and (len(str(number // divisor       )       ) == 3.0):
					return number
				divisor -= 1
	raise ValueError("""That number is larger than our acceptable range."""       )


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






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
_UpperCamelCase			       =			{
    '''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_(			snake_case__:  dict[str, list[str]]   )       -> set[tuple[str, str]]:
 UpperCAmelCase__							=				{node: {node} for node in graph}

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

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

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

  UpperCAmelCase__							=				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(snake_case__   )
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(snake_case__   )

    # Find cutset.
 UpperCAmelCase__							=				[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))



