

from math import ceil







def 		_lowercase (     lowercase__ = 1_0_0_1						):
      __lowerCAmelCase					:						Union[str, Any]					=					1

      for i in range(1   ,	int(ceil(n / 2.0						)						)						):
            __lowerCAmelCase					:						Dict					=					2 * i + 1
            __lowerCAmelCase					:						List[str]					=					2 * i
            __lowerCAmelCase					:						Any					=					total + 4 * odd**2 - 6 * even

      return total


if __name__ == "__main__":
 import sys

 if len(sys.argv) == 1:
  print(solution())
 else:
  try:
   _UpperCamelCase 			=		int(sys.argv[1])
   print(solution(n))
  except ValueError:
   print("Invalid entry - please enter a number")





import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)







class   __lowercase      (unittest.TestCase ):
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						List[str]					=					Vector([1, 2, 3]					)
       self.assertEqual(x.component(0					)      ,							1					)
       self.assertEqual(x.component(2					)      ,							3					)
       __lowerCAmelCase					:						Dict					=					Vector()
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Vector([0, 0, 0, 0, 0, 1]					)
       self.assertEqual(str(A_					)      ,							'''(0,0,0,0,0,1)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Union[str, Any]					=					Vector([1, 2, 3, 4]					)
       self.assertEqual(len(A_					)      ,							4					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Dict					=					Vector([1, 2]					)
       __lowerCAmelCase					:						Optional[int]					=					Vector([1, 2, 3, 4, 5]					)
       __lowerCAmelCase					:						Optional[Any]					=					Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]					)
       __lowerCAmelCase					:						str					=					Vector([1, -1, 1, -1, 2, -3, 4, -5]					)
       self.assertAlmostEqual(x.euclidean_length()      ,							2.236      ,							3					)
       self.assertAlmostEqual(y.euclidean_length()      ,							7.416      ,							3					)
       self.assertEqual(z.euclidean_length()      ,							0					)
       self.assertAlmostEqual(w.euclidean_length()      ,							7.616      ,							3					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						List[str]					=					Vector([1, 1, 1]					)
       self.assertEqual((x + y).component(0					)      ,							2					)
       self.assertEqual((x + y).component(1					)      ,							3					)
       self.assertEqual((x + y).component(2					)      ,							4					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						List[str]					=					Vector([1, 1, 1]					)
       self.assertEqual((x - y).component(0					)      ,							0					)
       self.assertEqual((x - y).component(1					)      ,							1					)
       self.assertEqual((x - y).component(2					)      ,							2					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						str					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						List[Any]					=					Vector([2, -1, 4]					)  # for test of dot product
       __lowerCAmelCase					:						Optional[int]					=					Vector([1, -2, -1]					)
       self.assertEqual(str(x * 3.0					)      ,							'''(3.0,6.0,9.0)'''					)
       self.assertEqual((a * b)      ,							0					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       self.assertEqual(str(zero_vector(10					)					).count('''0'''					)      ,							10					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       self.assertEqual(str(unit_basis_vector(3      ,							1					)					)      ,							'''(0,1,0)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						str					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						Any					=					Vector([1, 0, 1]					)
       self.assertEqual(str(axpy(2      ,							A_      ,							A_					)					)      ,							'''(3,4,7)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Vector([1, 0, 0, 0, 0, 0]					)
       __lowerCAmelCase					:						Optional[Any]					=					x.copy()
       self.assertEqual(str(A_					)      ,							str(A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						List[str]					=					Vector([1, 0, 0]					)
       x.change_component(0      ,							0					)
       x.change_component(1      ,							1					)
       self.assertEqual(str(A_					)      ,							'''(0,1,0)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Union[str, Any]					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       self.assertEqual('''|1,2,3|\n|2,4,5|\n|6,7,8|\n'''      ,							str(A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						List[Any]					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						str					=					[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
       for x in range(a.height()					):
             for y in range(a.width()					):
                   self.assertEqual(minors[x][y]      ,							a.minor(A_      ,							A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Optional[int]					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						Tuple					=					[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
       for x in range(a.height()					):
             for y in range(a.width()					):
                   self.assertEqual(cofactors[x][y]      ,							a.cofactor(A_      ,							A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Dict					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       self.assertEqual(-5      ,							a.determinant()					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]      ,							3      ,							3					)
       __lowerCAmelCase					:						Union[str, Any]					=					Vector([1, 2, 3]					)
       self.assertEqual('''(14,32,50)'''      ,							str(a * x					)					)
       self.assertEqual('''|2,4,6|\n|8,10,12|\n|14,16,18|\n'''      ,							str(a * 2					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       a.change_component(0      ,							2      ,							5					)
       self.assertEqual('''|1,2,5|\n|2,4,5|\n|6,7,8|\n'''      ,							str(A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       self.assertEqual(7      ,							a.component(2      ,							1					)      ,							0.01					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						Dict					=					Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]      ,							3      ,							3					)
       self.assertEqual('''|2,4,10|\n|4,8,10|\n|12,14,18|\n'''      ,							str(a + b					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Dict					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						str					=					Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]      ,							3      ,							3					)
       self.assertEqual('''|0,0,-4|\n|0,0,0|\n|0,0,-2|\n'''      ,							str(a - b					)					)





 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       self.assertEqual(
           '''|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n'''      ,							str(square_zero_matrix(5					)					)      ,							)


if __name__ == "__main__":
 unittest.main()


