

def  __lowerCAmelCase (  A      ):





	if len(_lowerCamelCase      ) == 0 or not all(len(_lowerCamelCase      ) == 2 for pair in coordinates      ):
		raise ValueError("The program cannot work out a fitting polynomial."      )

	if len({tuple(_lowerCamelCase      ) for pair in coordinates}      ) != len(_lowerCamelCase      ):
		raise ValueError("The program cannot work out a fitting polynomial."      )

	UpperCAmelCase_    			=     {x for x, _ in coordinates}
	if len(_lowerCamelCase      ) == 1:
		return F"x={coordinates[0][0]}"

	if len(_lowerCamelCase      ) != len(_lowerCamelCase      ):
		raise ValueError("The program cannot work out a fitting polynomial."      )

	UpperCAmelCase_    			=     len(_lowerCamelCase      )

	UpperCAmelCase_    			=     0
	UpperCAmelCase_    			=     []
	# put the x and x to the power values in a matrix
	while count_of_line < x:
		UpperCAmelCase_    			=     0
		UpperCAmelCase_    			=     coordinates[count_of_line][0]
		UpperCAmelCase_    			=     []
		while count_in_line < x:
			count_line.append(a ** (x - (count_in_line + 1))      )
			count_in_line += 1
		matrix.append(_lowerCamelCase      )
		count_of_line += 1

	UpperCAmelCase_    			=     0
	# put the y values into a vector
	UpperCAmelCase_    			=     []
	while count_of_line < x:
		vector.append(coordinates[count_of_line][1]      )
		count_of_line += 1

	UpperCAmelCase_    			=     0

	while count < x:
		UpperCAmelCase_    			=     0
		while zahlen < x:
			if count == zahlen:
				zahlen += 1
			if zahlen == x:
				break
			UpperCAmelCase_    			=     matrix[zahlen][count] / matrix[count][count]
			for counting_columns, item in enumerate(matrix[count]      ):
				# manipulating all the values in the matrix
				matrix[zahlen][counting_columns] -= item * bruch
			# manipulating the values in the vector
			vector[zahlen] -= vector[count] * bruch
			zahlen += 1
		count += 1

	UpperCAmelCase_    			=     0
	# make solutions
	UpperCAmelCase_    			=     []
	while count < x:
		solution.append(str(vector[count] / matrix[count][count]      )      )
		count += 1

	UpperCAmelCase_    			=     0
	UpperCAmelCase_    			=     "f(x)="

	while count < x:
		UpperCAmelCase_    			=     solution[count].split("E"      )
		if len(_lowerCamelCase      ) > 1:
			UpperCAmelCase_    			=     F"{remove_e[0]}*10^{remove_e[1]}"
		solved += F"x^{x - (count + 1)}*{solution[count]}"
		if count + 1 != x:
			solved += "+"
		count += 1

	return solved


if __name__ == "__main__":
				print(points_to_polynomial([]))
				print(points_to_polynomial([[]]))
				print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
				print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
				print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
				print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
				print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
				print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
				print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
				print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))


from string import ascii_uppercase



def  __lowerCAmelCase (  A    ,       A    ,       A = False    ,       A = ascii_uppercase      ):
	UpperCAmelCase_    			=     keyword.upper()
	UpperCAmelCase_    			=     plaintext.upper()
	UpperCAmelCase_    			=     set(A      )

	# create a list of unique characters in the keyword - their order matters
	# it determines how we will map plaintext characters to the ciphertext
	UpperCAmelCase_    			=     []
	for char in keyword:
		if char in alphabet_set and char not in unique_chars:
			unique_chars.append(A      )
    # the number of those unique characters will determine the number of rows
	UpperCAmelCase_    			=     len(A      )

	# create a shifted version of the alphabet
	UpperCAmelCase_    			=     unique_chars + [
	    char for char in alphabet if char not in unique_chars
	]

	# create a modified alphabet by splitting the shifted alphabet into rows
	UpperCAmelCase_    			=     [
	    shifted_alphabet[k : k + num_unique_chars_in_keyword]
	    for k in range(0    ,       26    ,       A      )
	]

	# map the alphabet characters to the modified alphabet characters
	# going 'vertically' through the modified alphabet - consider columns first
	UpperCAmelCase_    			=     {}
	UpperCAmelCase_    			=     0
	for column in range(A      ):
		for row in modified_alphabet:
			# if current row (the last one) is too short, break out of loop
			if len(A      ) <= column:
				break

			# map current letter to letter in modified alphabet
			UpperCAmelCase_    			=     row[column]
			letter_index += 1

	if verbose:
		print(A      )
	# create the encrypted text by mapping the plaintext to the modified alphabet
	return "".join(mapping[char] if char in mapping else char for char in plaintext      )


if __name__ == "__main__":
				# example use
				print(mixed_keyword("""college""", """UNIVERSITY"""))