






"""simple docstring"""





def 	lowerCAmelCase_(			SCREAMING_SNAKE_CASE       )       ->						list[int]:
    """simple docstring"""

    if len(SCREAMING_SNAKE_CASE       ) > 1:
        UpperCamelCase__								=     len(SCREAMING_SNAKE_CASE       ) // 2  # Finds the middle of the array
        UpperCamelCase__								=     arr[
            :middle_length
        ]  # Creates an array of the elements in the first half.
        UpperCamelCase__								=     arr[
            middle_length:
        ]  # Creates an array of the elements in the second half.
        UpperCamelCase__								=     len(SCREAMING_SNAKE_CASE       )
        UpperCamelCase__								=     len(SCREAMING_SNAKE_CASE       )
        merge(SCREAMING_SNAKE_CASE       )  # Starts sorting the left.
        merge(SCREAMING_SNAKE_CASE       )  # Starts sorting the right
        UpperCamelCase__								=     0  # Left Counter
        UpperCamelCase__								=     0  # Right Counter
        UpperCamelCase__								=     0  # Position Counter
        while (
            left_index < left_size and right_index < right_size
        ):  # Runs until the lowers size of the left and right are sorted.
            if left_array[left_index] < right_array[right_index]:
                UpperCamelCase__								=     left_array[left_index]
                left_index += 1
            else:
                UpperCamelCase__								=     right_array[right_index]
                right_index += 1
            index += 1
        while (
            left_index < left_size
        ):  # Adds the left over elements in the left half of the array
            UpperCamelCase__								=     left_array[left_index]
            left_index += 1
            index += 1
        while (
            right_index < right_size
        ):  # Adds the left over elements in the right half of the array
            UpperCamelCase__								=     right_array[right_index]
            right_index += 1
            index += 1
    return arr


if __name__ == "__main__":
  import doctest

  doctest.testmod()












"""simple docstring"""





from math import gcd







def 	lowerCAmelCase_(			SCREAMING_SNAKE_CASE = 1_20_00       )       ->						int:
    """simple docstring"""

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


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




