"""simple docstring"""






import sys

_A   					=    (
    '73167176531330624919225119674426574742355349194934'
    '96983520312774506326239578318016984801869478851843'
    '85861560789112949495459501737958331952853208805511'
    '12540698747158523863050715693290963295227443043557'
    '66896648950445244523161731856403098711121722383113'
    '62229893423380308135336276614282806444486645238749'
    '30358907296290491560440772390713810515859307960866'
    '70172427121883998797908792274921901699720888093776'
    '65727333001053367881220235421809751254540594752243'
    '52584907711670556013604839586446706324415722155397'
    '53697817977846174064955149290862569321978468622482'
    '83972241375657056057490261407972968652414535100474'
    '82166370484403199890008895243450658541227588666881'
    '16427171479924442928230863465674813919123162824586'
    '17866458359124566529476545682848912883142607690042'
    '24219022671055626321111109370544217506941658960408'
    '07198403850962455444362981230987879927244284909188'
    '84580156166097919133875499200524063689912560717606'
    '05886116467109405077541002256983155200055935729725'
    '71636269561882670428252483600823257530420752963450'
)




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase = N       )							->   int:
				SCREAMING_SNAKE_CASE__		  =				-sys.maxsize - 1
				for i in range(len(__UpperCAmelCase       ) - 12       ):
								SCREAMING_SNAKE_CASE__		  =				1
								for j in range(13       ):
												product *= int(n[i + j]       )
								if product > largest_product:
												SCREAMING_SNAKE_CASE__		  =				product
				return largest_product


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





"""simple docstring"""






# Logistic Regression from scratch

# In[62]:

# In[63]:

# importing all the required libraries

import numpy as np
from matplotlib import pyplot as plt
from sklearn import datasets




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   List[str]:
				return 1 / (1 + np.exp(-z       ))




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase       )							->   Dict:
				return (-y * np.log(__UpperCAmelCase       ) - (1 - y) * np.log(1 - h       )).mean()




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase       )							->   Any:
				SCREAMING_SNAKE_CASE__		  =				np.dot(__UpperCAmelCase  ,					__UpperCAmelCase       )
				return np.sum(y * scores - np.log(1 + np.exp(__UpperCAmelCase       )       )       )




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase=70_000       )							->   Optional[Any]:
				SCREAMING_SNAKE_CASE__		  =				np.zeros(x.shape[1]       )

				for iterations in range(__UpperCAmelCase       ):
								SCREAMING_SNAKE_CASE__		  =				np.dot(__UpperCAmelCase  ,					__UpperCAmelCase       )
								SCREAMING_SNAKE_CASE__		  =				sigmoid_function(__UpperCAmelCase       )
								SCREAMING_SNAKE_CASE__		  =				np.dot(x.T  ,					h - y       ) / y.size
								SCREAMING_SNAKE_CASE__		  =				theta - alpha * gradient  # updating the weights
								SCREAMING_SNAKE_CASE__		  =				np.dot(__UpperCAmelCase  ,					__UpperCAmelCase       )
								SCREAMING_SNAKE_CASE__		  =				sigmoid_function(__UpperCAmelCase       )
								SCREAMING_SNAKE_CASE__		  =				cost_function(__UpperCAmelCase  ,					__UpperCAmelCase       )
								if iterations % 100 == 0:
												print(F"""loss: {j} \t"""       )  # printing the loss after every 100 iterations
				return theta


# In[68]:

if __name__ == "__main__":
						_A   					=    datasets.load_iris()
						_A   					=    iris.data[:, :2]
						_A   					=    (iris.target != 0) * 1

						_A   					=    0.1
						_A   					=    logistic_reg(alpha, x, y, max_iterations=7_0_0_0_0)
						print('theta: ', theta)  # printing the theta i.e our weights vector




						def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   Union[str, Any]:
										return sigmoid_function(
										    np.dot(__UpperCAmelCase  ,					__UpperCAmelCase       )       )  # predicting the value of probability from the logistic regression algorithm

						plt.figure(figsize=(1_0, 6))
						plt.scatter(x[y == 0][:, 0], x[y == 0][:, 1], color='b', label='0')
						plt.scatter(x[y == 1][:, 0], x[y == 1][:, 1], color='r', label='1')
						((_A)					,			(_A))   					=    (x[:, 0].min(), x[:, 0].max())
						((_A)					,			(_A))   					=    (x[:, 1].min(), x[:, 1].max())
						((_A)					,			(_A))   					=    np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
						_A   					=    np.c_[xxa.ravel(), xxa.ravel()]
						_A   					=    predict_prob(grid).reshape(xxa.shape)
						plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='black')

						plt.legend()

						plt.show()




