"""simple docstring"""



from __future__ import annotations

def    _A(		lowerCAmelCase ,     lowerCAmelCase ,     lowerCAmelCase       ):
							if len(lowerCAmelCase       ) == 0:
														raise ValueError("""find_min() arg is an empty sequence"""       )
							if (
							    left >= len(lowerCAmelCase       )
							    or left < -len(lowerCAmelCase       )
							    or right >= len(lowerCAmelCase       )
							    or right < -len(lowerCAmelCase       )
							):
														raise IndexError("""list index out of range"""       )
							if left == right:
														return nums[left]
							A__					:    Any														= (left + right) >> 1  # the middle
							A__					:    Dict														= find_min(lowerCAmelCase ,     lowerCAmelCase ,     lowerCAmelCase       )  # find min in range[left, mid]
							A__					:    Any														= find_min(lowerCAmelCase ,     mid + 1 ,     lowerCAmelCase       )  # find min in range[mid + 1, right]

							return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)






"""simple docstring"""



def    _A(		lowerCAmelCase       ):
							if not isinstance(lowerCAmelCase ,     lowerCAmelCase       ):
														A__					:    int														= F'''Input value of [number={number}] must be an integer'''
														raise TypeError(lowerCAmelCase       )
							if number < 0 or number % 2 == 1:
														return False
							A__					:    List[Any]														= int(number**0.5       )
							return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
				import doctest

				doctest.testmod()





