




def 	_a      (						SCREAMING_SNAKE_CASE_							:				Optional[int]     ):
					__lowerCAmelCase				   =       []
					__lowerCAmelCase				   =       []
					__lowerCAmelCase				   =       {
					    "^": 3,
					    "*": 2,
					    "/": 2,
					    "%": 2,
					    "+": 1,
					    "-": 1,
					}  # Priority of each operator
					__lowerCAmelCase				   =       len(SCREAMING_SNAKE_CASE_     ) if (len(SCREAMING_SNAKE_CASE_     ) > 7) else 7

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

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

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

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

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







def 	_a      (						SCREAMING_SNAKE_CASE_							:				List[Any]     ):
					__lowerCAmelCase				   =       list(infix[::-1]     )  # reverse the infix equation

					for i in range(len(SCREAMING_SNAKE_CASE_     )     ):
										if infix[i] == "(":
															__lowerCAmelCase				   =       ")"  # change "(" to ")"
										elif infix[i] == ")":
															__lowerCAmelCase				   =       "("  # change ")" to "("

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


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










from queue import PriorityQueue
from typing import Any

import numpy as np







def 	_a      (						SCREAMING_SNAKE_CASE_							:				dict      ,      SCREAMING_SNAKE_CASE_							:				str      ,      SCREAMING_SNAKE_CASE_							:				set      ,      SCREAMING_SNAKE_CASE_							:				set      ,      SCREAMING_SNAKE_CASE_							:				dict      ,      SCREAMING_SNAKE_CASE_							:				dict      ,      SCREAMING_SNAKE_CASE_							:				PriorityQueue      ,      SCREAMING_SNAKE_CASE_							:				dict      ,      SCREAMING_SNAKE_CASE_							:				float | int      ,      ):
					for nxt, d in graph[v]:
										if nxt in visited_forward:
															continue
										__lowerCAmelCase				   =       cst_fwd.get(SCREAMING_SNAKE_CASE_      ,      np.inf     )
										__lowerCAmelCase				   =       cst_fwd[v] + d
										if new_cost_f < old_cost_f:
															queue.put((new_cost_f, nxt)     )
															__lowerCAmelCase				   =       new_cost_f
															__lowerCAmelCase				   =       v
										if nxt in visited_backward:
															if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
																				__lowerCAmelCase				   =       cst_fwd[v] + d + cst_bwd[nxt]
					return shortest_distance







def 	_a      (						SCREAMING_SNAKE_CASE_							:				str      ,      SCREAMING_SNAKE_CASE_							:				str      ,      SCREAMING_SNAKE_CASE_							:				dict      ,      SCREAMING_SNAKE_CASE_							:				dict     ):
					__lowerCAmelCase				   =       -1

					__lowerCAmelCase				   =       set()
					__lowerCAmelCase				   =       set()
					__lowerCAmelCase				   =       {source: 0}
					__lowerCAmelCase				   =       {destination: 0}
					__lowerCAmelCase				   =       {source: None}
					__lowerCAmelCase				   =       {destination: None}
					__lowerCAmelCase				   =       PriorityQueue()
					__lowerCAmelCase				   =       PriorityQueue()

					__lowerCAmelCase				   =       np.inf

					queue_forward.put((0, source)     )
					queue_backward.put((0, destination)     )

					if source == destination:
										return 0

					while not queue_forward.empty() and not queue_backward.empty():
										__lowerCAmelCase   ,							__lowerCAmelCase				   =       queue_forward.get()
										visited_forward.add(SCREAMING_SNAKE_CASE_     )

										__lowerCAmelCase   ,							__lowerCAmelCase				   =       queue_backward.get()
										visited_backward.add(SCREAMING_SNAKE_CASE_     )

										__lowerCAmelCase				   =       pass_and_relaxation(
										    SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      )

										__lowerCAmelCase				   =       pass_and_relaxation(
										    SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      )

										if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
															break

					if shortest_distance != np.inf:
										__lowerCAmelCase				   =       shortest_distance
					return shortest_path_distance


UpperCamelCase__    			=			{
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}
UpperCamelCase__    			=			{
    """B""": [["""E""", 1]],
    """C""": [["""B""", 1]],
    """D""": [["""C""", 1]],
    """F""": [["""D""", 1], ["""G""", 1]],
    """E""": [[None, np.inf]],
    """G""": [["""E""", 2]],
}

if __name__ == "__main__":
					import doctest

					doctest.testmod()




