


def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		lowercase__	     =						1  # To kept the Calculated Value
		# Since C(n, k) = C(n, n-k)
		if k > (n - k):
				lowercase__	     =						n - k
		# Calculate C(n,k)
		for i in range(__magic_name__	):
				result *= n - i
				result //= i + 1
		return result






def 					UpperCamelCase   (      __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		return binomial_coefficient(2 * node_count       ,       __magic_name__	) // (node_count + 1)






def 					UpperCamelCase   (      __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		if n < 0:
				raise ValueError("""factorial() not defined for negative values"""	)
		lowercase__	     =						1
		for i in range(1       ,       n + 1	):
				result *= i
		return result






def 					UpperCamelCase   (      __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		return catalan_number(__magic_name__	) * factorial(__magic_name__	)


if __name__ == "__main__":
	A			:						Tuple        =  int(input('Enter the number of nodes: ').strip() or 0)
	if node_count <= 0:
		raise ValueError('We need some nodes to work with.')
	print(
	    F'Given {node_count} nodes, there are {binary_tree_count(node_count)} '
	    F'binary trees and {catalan_number(node_count)} binary search trees.'
	)





from math import log

from scipy.constants import Boltzmann, physical_constants

A			:						Any        =  3_0_0  # TEMPERATURE (unit = K)






def 					UpperCamelCase   (      __magic_name__	:				float       ,       __magic_name__	:				float       ,       __magic_name__	:				float       ,       )  ->    float:
		"""simple docstring"""




		if donor_conc <= 0:
				raise ValueError("""Donor concentration should be positive"""	)
		elif acceptor_conc <= 0:
				raise ValueError("""Acceptor concentration should be positive"""	)
		elif intrinsic_conc <= 0:
				raise ValueError("""Intrinsic concentration should be positive"""	)
		elif donor_conc <= intrinsic_conc:
				raise ValueError(
				    """Donor concentration should be greater than intrinsic concentration"""	)
		elif acceptor_conc <= intrinsic_conc:
				raise ValueError(
				    """Acceptor concentration should be greater than intrinsic concentration"""	)
		else:
				return (
				    Boltzmann
				    * T
				    * log((donor_conc * acceptor_conc) / intrinsic_conc**2	)
				    / physical_constants["electron volt"][0]
				)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

