



def 	UpperCAmelCase__      (      UpperCAmelCase__ :float ,					UpperCAmelCase__ :float ,					UpperCAmelCase__ :float ,					UpperCAmelCase__ :float ,					UpperCAmelCase__ :float ,					)     ->   float:






 '''simple docstring'''

 a						=		[redshift, radiation_density, matter_density, dark_energy]
 if any(p < 0 for p in parameters					):
  raise ValueError("All input parameters must be positive"					)

 if any(p > 1 for p in parameters[1:4]					):
  raise ValueError("Relative densities cannot be greater than one"					)
 else:
  a						=		1 - (matter_density + radiation_density + dark_energy)

  a						=		(
      radiation_density * (redshift + 1) ** 4
      + matter_density * (redshift + 1) ** 3
      + curvature * (redshift + 1) ** 2
      + dark_energy
  )

  a						=		hubble_constant * e_a ** (1 / 2)
  return hubble


if __name__ == "__main__":
     import doctest

     # run doctest
     doctest.testmod()

     # demo LCDM approximation
     A_		:     str        =     0.3

     print(
         hubble_parameter(
             hubble_constant=68.3,
             radiation_density=1E-4,
             matter_density=matter_density,
             dark_energy=1 - matter_density,
             redshift=0,
         )
     )






def 	UpperCAmelCase__      (      UpperCAmelCase__ :Any					):






 '''simple docstring'''

 if not head:
  return True
 # split the list to two parts
 a		,  a						=		head.next, head
 while fast and fast.next:
  a						=		fast.next.next
  a						=		slow.next
 a						=		slow.next
 a						=		None  # Don't forget here! But forget still works!
 # reverse the second part
 a						=		None
 while second:
  a						=		second.next
  a						=		node
  a						=		second
  a						=		nxt
 # compare two parts
 # second part has the same or one less node
 while node:
  if node.val != head.val:
   return False
  a						=		node.next
  a						=		head.next
 return True


def 	UpperCAmelCase__      (      UpperCAmelCase__ :str					):






 '''simple docstring'''

 if not head or not head.next:
  return True

 # 1. Get the midpoint (slow)
 a						=		a						=		a						=		head
 while fast and fast.next:
  a		,  a						=		fast.next.next, slow.next

 # 2. Push the second half into the stack
 a						=		[slow.val]
 while slow.next:
  a						=		slow.next
  stack.append(slow.val					)

 # 3. Comparison
 while stack:
  if stack.pop() != cur.val:
   return False
  a						=		cur.next

 return True




def 	UpperCAmelCase__      (      UpperCAmelCase__ :Any					):






 '''simple docstring'''

 if not head or not head.next:
  return True
 a						=		{}
 a						=		0
 while head:
  if head.val in d:
   d[head.val].append(UpperCAmelCase__					)
  else:
   a						=		[pos]
  a						=		head.next
  pos += 1
 a						=		pos - 1
 a						=		0
 for v in d.values():
  if len(UpperCAmelCase__					) % 2 != 0:
   middle += 1
  else:
   a						=		0
   for i in range(0 ,					len(UpperCAmelCase__					)					):
    if v[i] + v[len(UpperCAmelCase__					) - 1 - step] != checksum:
     return False
    step += 1
  if middle > 1:
   return False
 return True

