






import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
		# Create universe of discourse in Python using linspace ()
		_a      	=  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).
		_a      	=  [0, 25, 50]
		_a      	=  [25, 50, 75]
		_a      	=  fuzz.membership.trimf(X, abca)
		_a      	=  fuzz.membership.trimf(X, abca)

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



from __future__ import annotations

from collections.abc import Generator


def   __SCREAMING_SNAKE_CASE					():
						snake_case_   =	{}
						snake_case_   =	2
						while True:
												snake_case_   =	factor_map.pop(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__       )
												if factor:
																		snake_case_   =	factor + prime
																		while x in factor_map:
																								x += factor
																		snake_case_   =	factor
												else:
																		snake_case_   =	prime
																		yield prime
												prime += 1


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__ = 1E10       ):
						snake_case_   =	sieve()

						snake_case_   =	1
						while True:
												snake_case_   =	next(SCREAMING_SNAKE_CASE__       )
												if (2 * prime * n) > limit:
																		return n
												# Ignore the next prime as the reminder will be 2.
												next(SCREAMING_SNAKE_CASE__       )
												n += 2


if __name__ == "__main__":
					print(solution())