



import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
						# Create universe of discourse in Python using linspace ()
						_snake_case	=						np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

						# Create two fuzzy sets by defining any membership function
						# (trapmf(), gbellmf(), gaussmf(), etc).
						_snake_case	=						[0, 25, 50]
						_snake_case	=						[25, 50, 75]
						_snake_case	=						fuzz.membership.trimf(X, abca)
						_snake_case	=						fuzz.membership.trimf(X, abca)

						# Compute the different operations using inbuilt functions.
						_snake_case	=						np.ones(75)
						_snake_case	=						np.zeros((75,))
						# 1. Union = max(µA(x), µB(x))
						_snake_case	=						fuzz.fuzzy_or(X, young, X, middle_aged)[1]
						# 2. Intersection = min(µA(x), µB(x))
						_snake_case	=						fuzz.fuzzy_and(X, young, X, middle_aged)[1]
						# 3. Complement (A) = (1- min(µA(x))
						_snake_case	=						fuzz.fuzzy_not(young)
						# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
						_snake_case	=						fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
						# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
						_snake_case	=						young + middle_aged - (young * middle_aged)
						# 6. Algebraic Product = (µA(x) * µB(x))
						_snake_case	=						young * middle_aged
						# 7. Bounded Sum = min[1,(µA(x), µB(x))]
						_snake_case	=						fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
						# 8. Bounded difference = min[0,(µA(x), µB(x))]
						_snake_case	=						fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

						# max-min composition
						# max-product composition

						# Plot each set A, set B and each operation result using plot() and subplot().
						from matplotlib import pyplot as plt

						plt.figure()

						plt.subplot(4, 3, 1)
						plt.plot(X, young)
						plt.title("Young")
						plt.grid(True)

						plt.subplot(4, 3, 2)
						plt.plot(X, middle_aged)
						plt.title("Middle aged")
						plt.grid(True)

						plt.subplot(4, 3, 3)
						plt.plot(X, union)
						plt.title("union")
						plt.grid(True)

						plt.subplot(4, 3, 4)
						plt.plot(X, intersection)
						plt.title("intersection")
						plt.grid(True)

						plt.subplot(4, 3, 5)
						plt.plot(X, complement_a)
						plt.title("complement_a")
						plt.grid(True)

						plt.subplot(4, 3, 6)
						plt.plot(X, difference)
						plt.title("difference a/b")
						plt.grid(True)

						plt.subplot(4, 3, 7)
						plt.plot(X, alg_sum)
						plt.title("alg_sum")
						plt.grid(True)

						plt.subplot(4, 3, 8)
						plt.plot(X, alg_product)
						plt.title("alg_product")
						plt.grid(True)

						plt.subplot(4, 3, 9)
						plt.plot(X, bdd_sum)
						plt.title("bdd_sum")
						plt.grid(True)

						plt.subplot(4, 3, 10)
						plt.plot(X, bdd_difference)
						plt.title("bdd_difference")
						plt.grid(True)

						plt.subplots_adjust(hspace=0.5)
						plt.show()





def        A       (      _lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							int				     =					len(_lowerCamelCase						)
							for i in range(1       ,				_lowerCamelCase						):
														_lowerCAmelCase  :							List[Any]				     =					collection[i]
														_lowerCAmelCase  :							str				     =					0
														_lowerCAmelCase  :							Union[str, Any]				     =					i - 1

														while low <= high:
																					_lowerCAmelCase  :							List[str]				     =					(low + high) // 2
																					if val < collection[mid]:
																												_lowerCAmelCase  :							Optional[int]				     =					mid - 1
																					else:
																												_lowerCAmelCase  :							List[str]				     =					mid + 1
														for j in range(_lowerCamelCase       ,				_lowerCamelCase       ,				-1						):
																					_lowerCAmelCase  :							int				     =					collection[j - 1]
														_lowerCAmelCase  :							Optional[int]				     =					val
							return collection


if __name__ == "__main__":
						_snake_case	=						input("Enter numbers separated by a comma:\n").strip()
						_snake_case	=						[int(item) for item in user_input.split(",")]
						print(binary_insertion_sort(unsorted))
