




from __future__ import annotations

from collections.abc import Callable

_lowerCamelCase     :		Optional[int]								=      list[list[float | int]]







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	Matrix:



       """simple docstring"""

       A__							=   len(lowercase_						)
       A__							=   [[0 for _ in range(size + 1						)] for _ in range(lowercase_						)]
       A__							=   42
       A__							=   42
       A__							=   42
       A__							=   42
       A__							=   42
       A__							=   42

       for row in range(lowercase_						):
              for col in range(lowercase_						):
                     A__							=   matrix[row][col]

              A__							=   vector[row][0]

       A__							=   0
       A__							=   0
       while row < size and col < size:
              # pivoting
              A__							=   max((abs(augmented[rowa][col]						), rowa) for rowa in range(lowercase_			,    lowercase_						)						)[
                  1
              ]
              if augmented[pivot_row][col] == 0:
                     col += 1
                     continue
              else:
                     A__			,							A__							=   augmented[pivot_row], augmented[row]

              for rowa in range(row + 1			,    lowercase_						):
                     A__							=   augmented[rowa][col] / augmented[row][col]
                     A__							=   0
                     for cola in range(col + 1			,    size + 1						):
                            augmented[rowa][cola] -= augmented[row][cola] * ratio

              row += 1
              col += 1

       # back substitution
       for col in range(1			,    lowercase_						):
              for row in range(lowercase_						):
                     A__							=   augmented[row][col] / augmented[col][col]
                     for cola in range(lowercase_			,    size + 1						):
                            augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
       return [
           [round(augmented[row][size] / augmented[row][row]			,    10						)] for row in range(lowercase_						)
       ]







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	Callable[[int], int]:



       """simple docstring"""

       A__							=   len(lowercase_						)
       A__							=   [[0 for _ in range(lowercase_						)] for _ in range(lowercase_						)]
       A__							=   [[0] for _ in range(lowercase_						)]
       A__							=   42
       A__							=   42
       A__							=   42
       A__							=   42

       for x_val, y_val in enumerate(lowercase_						):
              for col in range(lowercase_						):
                     A__							=   (x_val + 1) ** (size - col - 1)
              A__							=   y_val

       A__							=   solve(lowercase_			,    lowercase_						)

       def interpolated_func(lowercase_						) -> int:
              return sum(
                  round(coeffs[x_val][0]						) * (var ** (size - x_val - 1))
                  for x_val in range(lowercase_						)						)

       return interpolated_func







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	int:



       """simple docstring"""

       return (
           1
           - variable
           + variable**2
           - variable**3
           + variable**4
           - variable**5
           + variable**6
           - variable**7
           + variable**8
           - variable**9
           + variable**10
       )







def SCREAMING_SNAKE_CASE    (	lowercase_ = question_function			,    lowercase_ = 10						)       ->	int:



       """simple docstring"""

       A__							=   [func(lowercase_						) for x_val in range(1			,    order + 1						)]

       A__							=   [
           interpolate(data_points[:max_coeff]						) for max_coeff in range(1			,    order + 1						)
       ]

       A__							=   0
       A__							=   42
       A__							=   42

       for poly in polynomials:
              A__							=   1
              while func(lowercase_						) == poly(lowercase_						):
                     x_val += 1

              ret += poly(lowercase_						)

       return ret


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








def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	str:



       """simple docstring"""

       A__							=   []
       A__							=   []
       A__							=   {
           '''^''': 3,
           '''*''': 2,
           '''/''': 2,
           '''%''': 2,
           '''+''': 1,
           '''-''': 1,
       }  # Priority of each operator
       A__							=   len(lowercase_						) if (len(lowercase_						) > 7) else 7

       # Print table header for output
       print(
           '''Symbol'''.center(8						)			,    '''Stack'''.center(lowercase_						)			,    '''Postfix'''.center(lowercase_						)			,    sep=''' | '''			,    )
       print('''-''' * (print_width * 3 + 7)						)

       for x in infix:
              if x.isalpha() or x.isdigit():
                     post_fix.append(lowercase_						)  # if x is Alphabet / Digit, add it to Postfix
              elif x == "(":
                     stack.append(lowercase_						)  # if x is "(" push to Stack
              elif x == ")":  # if x is ")" pop stack until "(" is encountered
                     while stack[-1] != "(":
                            post_fix.append(stack.pop()						)  # Pop stack & add the content to Postfix
                     stack.pop()
              else:
                     if len(lowercase_						) == 0:
                            stack.append(lowercase_						)  # If stack is empty, push x to stack
                     else:  # while priority of x is not > priority of element in the stack
                            while len(lowercase_						) > 0 and priority[x] <= priority[stack[-1]]:
                                   post_fix.append(stack.pop()						)  # pop stack & add to Postfix
                            stack.append(lowercase_						)  # push x to stack

              print(
                  x.center(8						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    sep=''' | '''			,    )  # Output in tabular format

       while len(lowercase_						) > 0:  # while stack is not empty
              post_fix.append(stack.pop()						)  # pop stack & add to Postfix
              print(
                  ''' '''.center(8						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    sep=''' | '''			,    )  # Output in tabular format

       return "".join(lowercase_						)  # return Postfix as str







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	Optional[Any]:



       """simple docstring"""

       A__							=   list(infix[::-1]						)  # reverse the infix equation

       for i in range(len(lowercase_						)						):
              if infix[i] == "(":
                     A__							=   ''')'''  # change "(" to ")"
              elif infix[i] == ")":
                     A__							=   '''('''  # change ")" to "("

       return (infix_2_postfix(''''''.join(lowercase_						)						))[
           ::-1
       ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
  _lowerCamelCase     :		List[str]								=       input("""\nEnter an Infix Equation = """)  # Input an Infix equation
  _lowerCamelCase     :		Dict								=       """""".join(Infix.split())  # Remove spaces from the input
  print("""\n\t""", Infix, """(Infix) -> """, infix_2_prefix(Infix), """(Prefix)""")


