"""simple docstring"""




from collections import defaultdict
from math import ceil, sqrt





def 							SCREAMING_SNAKE_CASE  (    _lowerCamelCase		: int = 1000000    ,_lowerCamelCase		: int = 10			) ->   int:
  _lowerCAmelCase		: defaultdict						    =  defaultdict(_lowerCamelCase			)

  for outer_width in range(3    ,(t_limit // 4) + 2			):
    if outer_width * outer_width > t_limit:
      _lowerCAmelCase		: Union[str, Any]						    =  max(
          ceil(sqrt(outer_width * outer_width - t_limit			)			)    ,1			)
    else:
      _lowerCAmelCase		: Dict						    =  1

    hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

    for hole_width in range(_lowerCamelCase    ,outer_width - 1    ,2			):
      count[outer_width * outer_width - hole_width * hole_width] += 1

  return sum(1 for n in count.values() if 1 <= n <= 10			)


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





"""simple docstring"""




class 		__A							(				SCREAMING_SNAKE_CASE_	):
     pass







class 		__A							(				SCREAMING_SNAKE_CASE_	):
     pass







class 		__A							:






     def __init__(	self						):
       _lowerCAmelCase		: Union[str, Any]						    =  [
           [],
           [],
           [],
       ]






     def 					__A						(	self       ,  a__       ,  a__						):
       try:
         if len(self.queues[priority]						) >= 100:
           raise OverflowError("""Maximum queue size is 100"""						)
         self.queues[priority].append(a__						)
       except IndexError:
         raise ValueError("""Valid priorities are 0, 1, and 2"""						)






     def 					__A						(	self						):
       for queue in self.queues:
         if queue:
           return queue.pop(0						)
       raise UnderFlowError("""All queues are empty"""						)






     def __str__(	self						):
       return "\n".join(F"Priority {i}: {q}" for i, q in enumerate(self.queues						)						)







class 		__A							:






     def __init__(	self						):
       _lowerCAmelCase		: int						    =  []






     def 					__A						(	self       ,  a__						):
       if len(self.queue						) == 100:
         raise OverFlowError("""Maximum queue size is 100"""						)
       self.queue.append(a__						)






     def 					__A						(	self						):
       if not self.queue:
         raise UnderFlowError("""The queue is empty"""						)
       else:
         _lowerCAmelCase		: int						    =  min(self.queue						)
         self.queue.remove(a__						)
         return data






     def __str__(	self						):
       return str(self.queue						)







def 							SCREAMING_SNAKE_CASE  (    ) ->   str:
  _lowerCAmelCase		: Union[str, Any]						    =  FixedPriorityQueue()
  fpq.enqueue(0    ,10			)
  fpq.enqueue(1    ,70			)
  fpq.enqueue(0    ,100			)
  fpq.enqueue(2    ,1			)
  fpq.enqueue(2    ,5			)
  fpq.enqueue(1    ,7			)
  fpq.enqueue(2    ,4			)
  fpq.enqueue(1    ,64			)
  fpq.enqueue(0    ,128			)
  print(_lowerCamelCase			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(_lowerCamelCase			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)
  print(fpq.dequeue()			)





def 							SCREAMING_SNAKE_CASE  (    ) ->   Union[str, Any]:
  _lowerCAmelCase		: Tuple						    =  ElementPriorityQueue()
  epq.enqueue(10			)
  epq.enqueue(70			)
  epq.enqueue(100			)
  epq.enqueue(1			)
  epq.enqueue(5			)
  epq.enqueue(7			)
  epq.enqueue(4			)
  epq.enqueue(64			)
  epq.enqueue(128			)
  print(_lowerCamelCase			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(_lowerCamelCase			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)
  print(epq.dequeue()			)


if __name__ == "__main__":
     fixed_priority_queue()
     element_priority_queue()




