

from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
lowercase_									=   numpy.array([0, 0])
lowercase_									=   numpy.array([0.5, 0.8_6_6_0_2_5_4])
lowercase_									=   numpy.array([1, 0])
lowercase_									=   [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]
def      a      (			A__	:   list[numpy.ndarray]      ,   A__	:   int     )    ->      list[numpy.ndarray]:





      """simple docstring"""



      _lowercase	       =initial_vectors
      for _ in range(A__     ):
            _lowercase	       =iteration_step(A__     )
      return vectors
def      a      (			A__	:   list[numpy.ndarray]     )    ->      list[numpy.ndarray]:





      """simple docstring"""



      _lowercase	       =[]
      for i, start_vector in enumerate(vectors[:-1]     ):
            _lowercase	       =vectors[i + 1]
            new_vectors.append(A__     )
            _lowercase	       =end_vector - start_vector
            new_vectors.append(start_vector + difference_vector / 3     )
            new_vectors.append(
                start_vector + difference_vector / 3 + rotate(difference_vector / 3      ,   60     )     )
            new_vectors.append(start_vector + difference_vector * 2 / 3     )
      new_vectors.append(vectors[-1]     )
      return new_vectors
def      a      (			A__	:   numpy.ndarray      ,   A__	:   float     )    ->      numpy.ndarray:





      """simple docstring"""



      _lowercase	       =numpy.radians(A__     )
      _lowercase       ,       _lowercase	       =numpy.cos(A__     ), numpy.sin(A__     )
      _lowercase	       =numpy.array(((c, -s), (s, c))     )
      return numpy.dot(A__      ,   A__     )
def      a      (			A__	:   list[numpy.ndarray]     )    ->      None:





      """simple docstring"""



      _lowercase	       =plt.gca()
      axes.set_aspect('equal'     )

      # matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
      # y-coordinates as inputs, which are constructed from the vector-list using
      # zip()
      _lowercase       ,       _lowercase	       =zip(*A__     )
      plt.plot(A__      ,   A__     )
      plt.show()


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  lowercase_									=   iterate(INITIAL_VECTORS, 5)
  plot(processed_vectors)





import os
def      a      (			A__	:   str = "input.txt"     )    ->      int:





      """simple docstring"""



      with open(os.path.join(os.path.dirname(A__     )      ,   A__     )     ) as input_file:
            _lowercase	       =[
                [int(A__     ) for element in line.split(','     )]
                for line in input_file.readlines()
            ]

      _lowercase	       =len(A__     )
      _lowercase	       =len(matrix[0]     )

      _lowercase	       =[[-1 for _ in range(A__     )] for _ in range(A__     )]
      for i in range(A__     ):
            _lowercase	       =matrix[i][0]

      for j in range(1      ,   A__     ):
            for i in range(A__     ):
                  _lowercase	       =minimal_path_sums[i][j - 1] + matrix[i][j]

            for i in range(1      ,   A__     ):
                  _lowercase	       =min(
                      minimal_path_sums[i][j]      ,   minimal_path_sums[i - 1][j] + matrix[i][j]     )

            for i in range(rows - 2      ,   -1      ,   -1     ):
                  _lowercase	       =min(
                      minimal_path_sums[i][j]      ,   minimal_path_sums[i + 1][j] + matrix[i][j]     )

      return min(minimal_path_sums_row[-1] for minimal_path_sums_row in minimal_path_sums     )


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


