



from __future__ import annotations






def  lowerCamelCase_	(      lowerCAmelCase__	:	list[int]				)       ->							list[int]:

							'''simple docstring'''






							if len(lowerCAmelCase__				) == 0:
														return array

							A						,   A      						=    min(lowerCAmelCase__				), max(lowerCAmelCase__				)

							# Compute the variables
							A      						=    _max - _min + 1
							A						,   A      						=    [0] * holes_range, [0] * holes_range

							# Make the sorting.
							for i in array:
														A      						=    i - _min
														A      						=    i
														holes_repeat[index] += 1

							# Makes the array back by replacing the numbers.
							A      						=    0
							for i in range(lowerCAmelCase__				):
														while holes_repeat[i] > 0:
																					A      						=    holes[i]
																					index += 1
																					holes_repeat[i] -= 1

    # Returns the sorted array.
							return array


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				__snake_case     :Dict			       =input('Enter numbers separated by comma:\n')
				__snake_case     :Tuple			       =[int(x) for x in user_input.split(',')]
				print(pigeon_sort(unsorted))
"""simple docstring"""


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase = False		):







  """simple docstring"""
  if radian_mode:
    return [magnitude * cos(lowercase		), magnitude * sin(lowercase		)]
  return [magnitude * cos(radians(lowercase		)		), magnitude * sin(radians(lowercase		)		)]






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase = 10**-1		):







  """simple docstring"""
  _UpperCAmelCase    			=   cross(lowercase ,lowercase		)
  _UpperCAmelCase    			=   sum(lowercase		)
  return abs(lowercase		) < eps


if __name__ == "__main__":
    # Test to check if it works
    UpperCAmelCase__			=    array(
        [
            polar_force(718.4, 1_8_0 - 3_0),
            polar_force(879.54, 4_5),
            polar_force(1_0_0, -9_0),
        ]
    )

    UpperCAmelCase__			=    array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem 1 in image_data/2D_problems.jpg
    UpperCAmelCase__			=    array(
        [
            polar_force(3_0 * 9.81, 1_5),
            polar_force(2_1_5, 1_8_0 - 4_5),
            polar_force(2_6_4, 9_0 - 3_0),
        ]
    )

    UpperCAmelCase__			=    array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    UpperCAmelCase__			=    array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

    UpperCAmelCase__			=    array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()
