




def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list[int | float]]				)   ->					int:
      SCREAMING_SNAKE_CASE_      		=     len(__UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     len(matrix[0]				)
      SCREAMING_SNAKE_CASE_      		=     min(__UpperCAmelCase     ,     __UpperCAmelCase				)

      for row in range(__UpperCAmelCase				):
            # Check if diagonal element is not zero
            if matrix[row][row] != 0:
                  # Eliminate all the elements below the diagonal
                  for col in range(row + 1     ,     __UpperCAmelCase				):
                        SCREAMING_SNAKE_CASE_      		=     matrix[col][row] / matrix[row][row]
                        for i in range(__UpperCAmelCase     ,     __UpperCAmelCase				):
                              matrix[col][i] -= multiplier * matrix[row][i]
            else:
                  # Find a non-zero diagonal element to swap rows
                  SCREAMING_SNAKE_CASE_      		=     True
                  for i in range(row + 1     ,     __UpperCAmelCase				):
                        if matrix[i][row] != 0:
                              SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_      		=     matrix[i], matrix[row]
                              SCREAMING_SNAKE_CASE_      		=     False
                              break
                  if reduce:
                        rank -= 1
                        for i in range(__UpperCAmelCase				):
                              SCREAMING_SNAKE_CASE_      		=     matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
                  row -= 1

      return rank


if __name__ == "__main__":
   import doctest

   doctest.testmod()





from __future__ import annotations

from collections.abc import Iterator





class 			lowerCamelCase_				:


 '''simple docstring'''







 def __init__(				self    :						Union[str, Any]							,							_lowerCAmelCase    :						int		):
       SCREAMING_SNAKE_CASE_      		=     value
       SCREAMING_SNAKE_CASE_      		=     None
       SCREAMING_SNAKE_CASE_      		=     None





class 			lowerCamelCase_				:


 '''simple docstring'''







 def __init__(				self    :						int							,							_lowerCAmelCase    :						Node		):
       SCREAMING_SNAKE_CASE_      		=     tree



 def  lowerCAmelCase_    (				self    :						Union[str, Any]							,							_lowerCAmelCase    :						Node | None		):
       if node is None:
             return 0
       return node.value + (
           self.depth_first_search(node.left		) + self.depth_first_search(node.right		)
       )




 def __iter__(				self    :						Dict		):
       yield self.depth_first_search(self.tree		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()