




"""simple docstring"""







from collections import defaultdict
from math import gcd





def 							lowercase					(snake_case__   : int = 1_500_000 )     ->  int:


				'''simple docstring'''






				lowerCAmelCase  =				defaultdict(snake_case__ )
				lowerCAmelCase  =				2
				while 2 * euclid_m * (euclid_m + 1) <= limit:
								for euclid_n in range((euclid_m % 2) + 1      ,       snake_case__      ,       2 ):
												if gcd(snake_case__      ,       snake_case__ ) > 1:
																continue
												lowerCAmelCase  =				2 * euclid_m * (euclid_m + euclid_n)
												for perimeter in range(snake_case__      ,       limit + 1      ,       snake_case__ ):
																frequencies[perimeter] += 1
								euclid_m += 1
				return sum(1 for frequency in frequencies.values() if frequency == 1 )


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











"""simple docstring"""







from queue import PriorityQueue
from typing import Any

import numpy as np





def 							lowercase					(snake_case__   : dict      ,       snake_case__   : str      ,       snake_case__   : set      ,       snake_case__   : set      ,       snake_case__   : dict      ,       snake_case__   : dict      ,       snake_case__   : PriorityQueue      ,       snake_case__   : dict      ,       snake_case__   : float | int      ,       )     ->  float | int:


				'''simple docstring'''






				for nxt, d in graph[v]:
								if nxt in visited_forward:
												continue
								lowerCAmelCase  =				cst_fwd.get(snake_case__      ,       np.inf )
								lowerCAmelCase  =				cst_fwd[v] + d
								if new_cost_f < old_cost_f:
												queue.put((new_cost_f, nxt) )
												lowerCAmelCase  =				new_cost_f
												lowerCAmelCase  =				v
								if nxt in visited_backward:
												if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
																lowerCAmelCase  =				cst_fwd[v] + d + cst_bwd[nxt]
				return shortest_distance





def 							lowercase					(snake_case__   : str      ,       snake_case__   : str      ,       snake_case__   : dict      ,       snake_case__   : dict )     ->  int:


				'''simple docstring'''






				lowerCAmelCase  =				-1

				lowerCAmelCase  =				set()
				lowerCAmelCase  =				set()
				lowerCAmelCase  =				{source: 0}
				lowerCAmelCase  =				{destination: 0}
				lowerCAmelCase  =				{source: None}
				lowerCAmelCase  =				{destination: None}
				lowerCAmelCase  =				PriorityQueue()
				lowerCAmelCase  =				PriorityQueue()

				lowerCAmelCase  =				np.inf

				queue_forward.put((0, source) )
				queue_backward.put((0, destination) )

				if source == destination:
								return 0

				while not queue_forward.empty() and not queue_backward.empty():
								lowerCAmelCase ,						lowerCAmelCase  =				queue_forward.get()
								visited_forward.add(snake_case__ )

								lowerCAmelCase ,						lowerCAmelCase  =				queue_backward.get()
								visited_backward.add(snake_case__ )

								lowerCAmelCase  =				pass_and_relaxation(
								    snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       )

								lowerCAmelCase  =				pass_and_relaxation(
								    snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       )

								if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
												break

				if shortest_distance != np.inf:
								lowerCAmelCase  =				shortest_distance
				return shortest_path_distance


a      =							{
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
a      =							{
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
		import doctest

		doctest.testmod()





