'''simple docstring'''




from numpy import exp, pi, sqrt






def 				snake_case__							(			_A:					Tuple      ,   _A:					float = 0.0      ,   _A:					float = 1.0 )    ->	int:

		'''simple docstring'''


		return 1 / sqrt(2 * pi * sigma**2 ) * exp(-((x - mu) ** 2) / (2 * sigma**2) )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





'''simple docstring'''




def 				snake_case__							(			_A:					str )    ->	list[int]:

		'''simple docstring'''


		lowerCAmelCase   					=  [0 for i in range(len(_A ) )]

		# initialize interval's left pointer and right pointer
		lowerCAmelCase					,     lowerCAmelCase   					=  0, 0

		for i in range(1      ,   len(_A ) ):
				# case when current index is inside the interval
				if i <= right_pointer:
						lowerCAmelCase   					=  min(right_pointer - i + 1      ,   z_result[i - left_pointer] )
						lowerCAmelCase   					=  min_edge

				while go_next(_A      ,   _A      ,   _A ):
						z_result[i] += 1

				# if new index's result gives us more right interval,
				# we've to update left_pointer and right_pointer
				if i + z_result[i] - 1 > right_pointer:
						lowerCAmelCase					,     lowerCAmelCase   					=  i, i + z_result[i] - 1

		return z_result






def 				snake_case__							(			_A:					int      ,   _A:					list[int]      ,   _A:					str )    ->	bool:

		'''simple docstring'''


		return i + z_result[i] < len(_A ) and s[z_result[i]] == s[i + z_result[i]]






def 				snake_case__							(			_A:					str      ,   _A:					str )    ->	int:

		'''simple docstring'''


		lowerCAmelCase   					=  0
		# concatenate 'pattern' and 'input_str' and call z_function
		# with concatenated string
		lowerCAmelCase   					=  z_function(pattern + input_str )

		for val in z_result:
				# if value is greater then length of the pattern string
				# that means this index is starting position of substring
				# which is equal to pattern string
				if val >= len(_A ):
						answer += 1

		return answer


if __name__ == "__main__":
						import doctest

						doctest.testmod()




