code: 
  
  import os
  
  
  def       __a       (   )      ->     Dict:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			os.path.dirname(os.path.realpath(SCREAMING_SNAKE_CASE      )      )
      __UpperCAmelCase									=			os.path.join(SCREAMING_SNAKE_CASE       ,   '''triangle.txt'''      )
  
      with open(SCREAMING_SNAKE_CASE      ) as f:
          __UpperCAmelCase									=			f.readlines()
  
      __UpperCAmelCase									=			[[int(SCREAMING_SNAKE_CASE      ) for y in x.rstrip('''\r\n'''      ).split(''' '''      )] for x in triangle]
  
      for i in range(1       ,   len(SCREAMING_SNAKE_CASE      )      ):
          for j in range(len(a[i]      )      ):
              __UpperCAmelCase									=			a[i - 1][j] if j != len(a[i - 1]      ) else 0
              __UpperCAmelCase									=			a[i - 1][j - 1] if j > 0 else 0
              a[i][j] += max(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
      return max(a[-1]      )
  
  
  if __name__ == "__main__":
         print(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()
  
  
  
  
  