





from math import sqrt



def _a				(	lowerCamelCase:   int )	->						bool:







      '''simple docstring'''






      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5					,				int(sqrt(lowerCamelCase ) + 1 )					,				6 ):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True



def _a				(	lowerCamelCase:   int = 1_00_01 )	->						int:







      '''simple docstring'''






      __A          =				0
      __A          =				1
      while count != nth and number < 3:
            number += 1
            if is_prime(lowerCamelCase ):
                  count += 1
      while count != nth:
            number += 2
            if is_prime(lowerCamelCase ):
                  count += 1
      return number


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












from __future__ import annotations



def _a				(	lowerCamelCase:   list[float]					,				lowerCamelCase:   Tuple )	->						List[str]:







      '''simple docstring'''






      print(F"""Vertex\tShortest Distance from vertex {src}""" )
      for i, d in enumerate(lowerCamelCase ):
            print(F"""{i}\t\t{d}""" )



def _a				(	lowerCamelCase:   list[dict[str, int]]					,				lowerCamelCase:   list[float]					,				lowerCamelCase:   int )	->						Union[str, Any]:







      '''simple docstring'''






      for j in range(lowerCamelCase ):
            __A   ,						__A   ,						__A          =				(graph[j][k] for k in ['''src''', '''dst''', '''weight'''])
            if distance[u] != float('''inf''' ) and distance[u] + w < distance[v]:
                  return True
      return False



def _a				(	lowerCamelCase:   list[dict[str, int]]					,				lowerCamelCase:   int					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						list[float]:







      '''simple docstring'''






      __A          =				[float('''inf''' )] * vertex_count
      __A          =				0.0

      for _ in range(vertex_count - 1 ):
            for j in range(lowerCamelCase ):
                  __A   ,						__A   ,						__A          =				(graph[j][k] for k in ['''src''', '''dst''', '''weight'''])

                  if distance[u] != float('''inf''' ) and distance[u] + w < distance[v]:
                        __A          =				distance[u] + w

      __A          =				check_negative_cycle(lowerCamelCase					,				lowerCamelCase					,				lowerCamelCase )
      if negative_cycle_exists:
            raise Exception('''Negative cycle found''' )

      return distance


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       snake_case__					:							Dict													=     int(input('Enter number of vertices: ').strip())
       snake_case__					:							Optional[int]													=     int(input('Enter number of edges: ').strip())

       snake_case__					:							list[dict[str, int]]													=     [{} for _ in range(E)]

       for i in range(E):
              print('Edge ', i + 1)
              snake_case__						,    snake_case__						,    snake_case__					:							Dict													=     (
                  int(x)
                  for x in input('Enter source, destination, weight: ').strip().split(' ')
              )
              snake_case__					:							List[Any]													=     {'src': src, 'dst': dest, 'weight': weight}

       snake_case__					:							Union[str, Any]													=     int(input('\nEnter shortest path source:').strip())
       snake_case__					:							List[Any]													=     bellman_ford(graph, V, E, source)
       print_distance(shortest_distance, 0)





