
"""simple docstring"""

def     lowercase__						(					lowerCAmelCase				:					str ,				lowerCAmelCase				:					str ) ->      int:






    """simple docstring"""




    assert x is not None
    assert y is not None

    UpperCAmelCase									=					len(lowerCAmelCase )
    UpperCAmelCase									=					len(lowerCAmelCase )

    # declaring the array for storing the dp values
    UpperCAmelCase									=					[[0] * (n + 1) for _ in range(m + 1 )]  # noqa: E741

    for i in range(1 ,				m + 1 ):
        for j in range(1 ,				n + 1 ):
            UpperCAmelCase									=					1 if x[i - 1] == y[j - 1] else 0

            UpperCAmelCase									=					max(l[i - 1][j] ,				l[i][j - 1] ,				l[i - 1][j - 1] + match )

    UpperCAmelCase									=					''
    UpperCAmelCase			,							UpperCAmelCase									=					m, n
    while i > 0 and j > 0:
        UpperCAmelCase									=					1 if x[i - 1] == y[j - 1] else 0

        if l[i][j] == l[i - 1][j - 1] + match:
            if match == 1:
                UpperCAmelCase									=					x[i - 1] + seq
            i -= 1
            j -= 1
        elif l[i][j] == l[i - 1][j]:
            i -= 1
        else:
            j -= 1

    return l[m][n], seq


if __name__ == "__main__":
   SCREAMING_SNAKE_CASE_    					=						'''AGGTAB'''
   SCREAMING_SNAKE_CASE_    					=						'''GXTXAYB'''
   SCREAMING_SNAKE_CASE_    					=						4
   SCREAMING_SNAKE_CASE_    					=						'''GTAB'''

   SCREAMING_SNAKE_CASE_					,						SCREAMING_SNAKE_CASE_    					=						longest_common_subsequence(a, b)
   print('''len =''', ln, ''', sub-sequence =''', subseq)
   import doctest

   doctest.testmod()





"""simple docstring"""

import sys
import turtle




def     lowercase__						(					lowerCAmelCase				:					tuple[float, float] ,				lowerCAmelCase				:					tuple[float, float] ) ->      tuple[float, float]:






    """simple docstring"""




    return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2




def     lowercase__						(					lowerCAmelCase				:					tuple[float, float] ,				lowerCAmelCase				:					tuple[float, float] ,				lowerCAmelCase				:					tuple[float, float] ,				lowerCAmelCase				:					int ,				) ->      None:






    """simple docstring"""




    my_pen.up()
    my_pen.goto(vertexa[0] ,				vertexa[1] )
    my_pen.down()
    my_pen.goto(vertexa[0] ,				vertexa[1] )
    my_pen.goto(vertexa[0] ,				vertexa[1] )
    my_pen.goto(vertexa[0] ,				vertexa[1] )

    if depth == 0:
        return

    triangle(lowerCAmelCase ,				get_mid(lowerCAmelCase ,				lowerCAmelCase ) ,				get_mid(lowerCAmelCase ,				lowerCAmelCase ) ,				depth - 1 )
    triangle(lowerCAmelCase ,				get_mid(lowerCAmelCase ,				lowerCAmelCase ) ,				get_mid(lowerCAmelCase ,				lowerCAmelCase ) ,				depth - 1 )
    triangle(lowerCAmelCase ,				get_mid(lowerCAmelCase ,				lowerCAmelCase ) ,				get_mid(lowerCAmelCase ,				lowerCAmelCase ) ,				depth - 1 )


if __name__ == "__main__":
   if len(sys.argv) != 2:
      raise ValueError(
          '''Correct format for using this script: '''
          '''python fractals.py <int:depth_for_fractal>'''
      )
   SCREAMING_SNAKE_CASE_    					=						turtle.Turtle()
   my_pen.ht()
   my_pen.speed(5)
   my_pen.pencolor('''red''')

   SCREAMING_SNAKE_CASE_    					=						[(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
   triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))



