



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 math import sqrt
def   _UpperCamelCase				(						lowerCAmelCase_ = 1_0_0_0_0_0_0   )						->int:
   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   UpperCAmelCase							=     42

   while num_cuboids <= limit:
      max_cuboid_size += 1
      for sum_shortest_sides in range(2  ,						2 * max_cuboid_size + 1   ):
         if sqrt(sum_shortest_sides**2 + max_cuboid_size**2   ).is_integer():
            num_cuboids += (
                min(lowerCAmelCase_  ,						sum_shortest_sides // 2   )
                - max(1  ,						sum_shortest_sides - max_cuboid_size   )
                + 1
            )

   return max_cuboid_size


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



