import heapq

def 				UpperCamelCase					(     lowerCAmelCase_							,       lowerCAmelCase_							,       lowerCAmelCase_ )		->    Dict:




       '''simple docstring'''






       _A=						[(0, start)]  # cost from start node,end node
       _A=						set()
       while heap:
              ((_A),      (_A))=						heapq.heappop(lowerCAmelCase_ )
              if u in visited:
                     continue
              visited.add(lowerCAmelCase_ )
              if u == end:
                     return cost
              for v, c in graph[u]:
                     if v in visited:
                            continue
                     _A=						cost + c
                     heapq.heappush(lowerCAmelCase_							,       (next_item, v) )
       return -1


UpperCAmelCase_    		=				{
    '''A''': [['''B''', 2], ['''C''', 5]],
    '''B''': [['''A''', 2], ['''D''', 3], ['''E''', 1], ['''F''', 1]],
    '''C''': [['''A''', 5], ['''F''', 3]],
    '''D''': [['''B''', 3]],
    '''E''': [['''B''', 4], ['''F''', 3]],
    '''F''': [['''C''', 3], ['''E''', 3]],
}
UpperCAmelCase_    		=				{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''F''', 3]],
    '''F''': [],
}
UpperCAmelCase_    		=				{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}

UpperCAmelCase_    		=				dijkstra(G, '''E''', '''C''')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

UpperCAmelCase_    		=				dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 3 --> F == 3

UpperCAmelCase_    		=				dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
      import doctest

      doctest.testmod()
from __future__ import annotations

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    set[int]:




       '''simple docstring'''






       _A=						{1}
       _A=						[1]
       for _ in range(2							,       depth + 1 ):
              _A=						[*previous_coefficients, 0]
              _A=						[0, *previous_coefficients]
              _A=						[]
              for x, y in zip(lowerCAmelCase_							,       lowerCAmelCase_ ):
                     coefficients.add(x + y )
                     previous_coefficients.append(x + y )
       return coefficients

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    set[int]:




       '''simple docstring'''






       _A=						set()
       for number in unique_coefficients:
              _A=						2
              _A=						number
              while divisor**2 <= copy_number:
                     _A=						0
                     while copy_number % divisor == 0:
                            copy_number //= divisor
                            multiplicity += 1
                     if multiplicity >= 2:
                            non_squarefrees.add(lowerCAmelCase_ )
                            break
                     divisor += 1

       return unique_coefficients.difference(lowerCAmelCase_ )

def 				UpperCamelCase					(     lowerCAmelCase_ = 51 )		->    int:




       '''simple docstring'''






       _A=						get_pascal_triangle_unique_coefficients(lowerCAmelCase_ )
       _A=						get_squarefrees(lowerCAmelCase_ )
       return sum(lowerCAmelCase_ )


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