

import math
from timeit import timeit



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				A__            =     0
				A__            =     abs(SCREAMING_SNAKE_CASE_ )
				while True:
								A__            =     n // 1_0
								digits += 1
								if n == 0:
												break
				return digits



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				return 1 if n == 0 else math.floor(math.log(abs(SCREAMING_SNAKE_CASE_ )		,    1_0 ) + 1 )



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				return len(str(abs(SCREAMING_SNAKE_CASE_ ) ) )



def    lowerCAmelCase__							(		)     -> None:




				'''simple docstring'''





				from collections.abc import Callable

				def benchmark_a_function(SCREAMING_SNAKE_CASE_:							Callable		,    SCREAMING_SNAKE_CASE_:							int ) -> None:
								A__            =     F'{func.__name__}({value})'
								A__            =     timeit(F'__main__.{call}'		,    setup="import __main__" )
								print(F'{call}: {func(SCREAMING_SNAKE_CASE_ )} -- {timing} seconds' )

				for value in (2_6_2_1_4_4, 1_1_2_5_8_9_9_9_0_6_8_4_2_6_2_4, 1_2_6_7_6_5_0_6_0_0_2_2_8_2_2_9_4_0_1_4_9_6_7_0_3_2_0_5_3_7_6):
								for func in (num_digits, num_digits_fast, num_digits_faster):
												benchmark_a_function(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )
								print()


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	benchmark()




from .balanced_parentheses import balanced_parentheses
from .stack import Stack



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							str )     -> int:




				'''simple docstring'''





				return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(SCREAMING_SNAKE_CASE_		,    -1 )



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							str )     -> str:




				'''simple docstring'''





				if not balanced_parentheses(SCREAMING_SNAKE_CASE_ ):
								raise ValueError("Mismatched parentheses" )
				A__            =     Stack()
				A__            =     []
				for char in expression_str:
								if char.isalpha() or char.isdigit():
												postfix.append(SCREAMING_SNAKE_CASE_ )
								elif char == "(":
												stack.push(SCREAMING_SNAKE_CASE_ )
								elif char == ")":
												while not stack.is_empty() and stack.peek() != "(":
																postfix.append(stack.pop() )
												stack.pop()
								else:
												while not stack.is_empty() and precedence(SCREAMING_SNAKE_CASE_ ) <= precedence(stack.peek() ):
																postfix.append(stack.pop() )
												stack.push(SCREAMING_SNAKE_CASE_ )
				while not stack.is_empty():
								postfix.append(stack.pop() )
				return " ".join(SCREAMING_SNAKE_CASE_ )


if __name__ == "__main__":
	from doctest import testmod

	testmod()
	lowerCAmelCase__						=	"""a+b*(c^d-e)^(f+g*h)-i"""

	print("""Infix to Postfix Notation demonstration:\n""")
	print("""Infix notation: """ + expression)
	print("""Postfix notation: """ + infix_to_postfix(expression))

