

from math import gcd
def 		_snake_case(       SCREAMING_SNAKE_CASE__     :      int = 12000 )				-> Optional[int]:





    '''simple docstring'''






    A__        =  0
    for d in range(max_d + 1 ):
        for n in range(d // 3 + 1       ,     (d + 1) // 2 ):
            if gcd(_lowerCAmelCase       ,     _lowerCAmelCase ) == 1:
                fractions_number += 1
    return fractions_number


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







from math import cos, sin



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 UpperCAmelCase__							=    float(_lowerCAmelCase						)
 return [[scaling_factor * int(x == y						) for x in range(2						)] for y in range(2						)]



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 UpperCAmelCase__			,			UpperCAmelCase__							=    cos(_lowerCAmelCase						), sin(_lowerCAmelCase						)
 return [[c, -s], [s, c]]



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 UpperCAmelCase__			,			UpperCAmelCase__							=    cos(_lowerCAmelCase						), sin(_lowerCAmelCase						)
 UpperCAmelCase__							=    c * s
 return [[c * c, cs], [cs, s * s]]



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 UpperCAmelCase__			,			UpperCAmelCase__							=    cos(_lowerCAmelCase						), sin(_lowerCAmelCase						)
 UpperCAmelCase__							=    c * s
 return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F'''    {scaling(5) = }''')
print(F'''  {rotation(4_5) = }''')
print(F'''{projection(4_5) = }''')


print(F'''{reflection(4_5) = }''')





