



'''simple docstring'''


def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     if divisor % 5 == 0 or divisor % 2 == 0:
          return 0
     a_       		=1
     a_       		=1
     while repunit:
          a_       		=(1_0 * repunit + 1) % divisor
          repunit_index += 1
     return repunit_index






def  UpperCAmelCase_       (		lowercase__ = 1_0_0_0_0_0_0       ):


     '''simple docstring'''







     a_       		=limit - 1
     if divisor % 2 == 0:
          divisor += 1
     while least_divisible_repunit(lowercase__       ) <= limit:
          divisor += 2
     return divisor


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







'''simple docstring'''


from typing import Any

import numpy as np






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     return np.array_equal(lowercase__       ,	matrix.conjugate().T       )






def  UpperCAmelCase_       (		lowercase__       ,	lowercase__       ):


     '''simple docstring'''







     a_       		=v.conjugate().T
     a_       		=v_star.dot(lowercase__       )
     assert isinstance(lowercase__       ,	np.ndarray       )
     return (v_star_dot.dot(lowercase__       )) / (v_star.dot(lowercase__       ))






def  UpperCAmelCase_       (		):


     '''simple docstring'''







     a_       		=np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]       )
     a_       		=np.array([[1], [2], [3]]       )
     assert is_hermitian(lowercase__       ), F"""{a} is not hermitian."""
     print(rayleigh_quotient(lowercase__       ,	lowercase__       )       )

     a_       		=np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]       )
     assert is_hermitian(lowercase__       ), F"""{a} is not hermitian."""
     assert rayleigh_quotient(lowercase__       ,	lowercase__       ) == float(3       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  tests()


