code: 
  
  def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )      ->     int:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			1.0
      for i in range(1       ,   r + 1      ):
          ret *= (n + 1 - i) / i
      return round(SCREAMING_SNAKE_CASE      )
  
  
  def       __a       (   SCREAMING_SNAKE_CASE      )      ->     int:
  
  
  
  
  
  
      '''simple docstring'''
      return choose(8 + n       ,   SCREAMING_SNAKE_CASE      ) + choose(9 + n       ,   SCREAMING_SNAKE_CASE      ) - 1_0
  
  
  def       __a       (   SCREAMING_SNAKE_CASE      )      ->     int:
  
  
  
  
  
  
      '''simple docstring'''
      return sum(non_bouncy_exact(SCREAMING_SNAKE_CASE      ) for i in range(1       ,   n + 1      )      )
  
  
  def       __a       (   SCREAMING_SNAKE_CASE = 1_0_0      )      ->     int:
  
  
  
  
  
  
      '''simple docstring'''
      return non_bouncy_upto(SCREAMING_SNAKE_CASE      )
  
  
  if __name__ == "__main__":
         print(F"""{solution() = }""")
  
  
  
  
  
style_context: 
  
  import numpy as np
  
  
  def       __a       (   SCREAMING_SNAKE_CASE      )      ->     Tuple:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase					,     __UpperCAmelCase									=			a.shape
      __UpperCAmelCase									=			min(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			np.eye(SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			a.copy()
  
      for k in range(t - 1      ):
          # select a column of modified matrix A':
          __UpperCAmelCase									=			r[k:, [k]]
          # construct first basis vector
          __UpperCAmelCase									=			np.zeros_like(SCREAMING_SNAKE_CASE      )
          __UpperCAmelCase									=			1.0
          # determine scaling factor
          __UpperCAmelCase									=			np.linalg.norm(SCREAMING_SNAKE_CASE      )
          # construct vector v for Householder reflection
          __UpperCAmelCase									=			x + np.sign(x[0]      ) * alpha * ea
          v /= np.linalg.norm(SCREAMING_SNAKE_CASE      )
  
          # construct the Householder matrix
          __UpperCAmelCase									=			np.eye(m - k      ) - 2.0 * v @ v.T
          # pad with ones and zeros as necessary
          __UpperCAmelCase									=			np.block([[np.eye(SCREAMING_SNAKE_CASE      ), np.zeros((k, m - k)      )], [np.zeros((m - k, k)      ), q_k]]      )
  
          __UpperCAmelCase									=			q @ q_k.T
          __UpperCAmelCase									=			q_k @ r
  
      return q, r
  
  
  if __name__ == "__main__":
         import doctest
  
         doctest.testmod()
  
  
  
  
  