"""
The nested brackets problem is a problem that determines if a sequence of
brackets are properly nested. A sequence of brackets s is considered properly nested
if any of the following conditions are true:

 - s is empty
 - s has the form (U) or [U] or {U} where U is a properly nested string
 - s has the form VW where V and W are properly nested strings

For example, the string "()()[()]" is properly nested but "[(()]" is not.

The function called is_balanced takes as input a string S which is a sequence of
brackets and returns true if S is nested and false otherwise.
"""


def is_balanced(s: str) -> bool:
 """
 >>> is_balanced("")
 True
 >>> is_balanced("()")
 True
 >>> is_balanced("[]")
 True
 >>> is_balanced("{}")
 True
 >>> is_balanced("()[]{}")
 True
 >>> is_balanced("(())")
 True
 >>> is_balanced("[[")
 False
 >>> is_balanced("([{}])")
 True
 >>> is_balanced("(()[)]")
 False
 >>> is_balanced("([)]")
 False
 >>> is_balanced("[[()]]")
 True
 >>> is_balanced("(()(()))")
 True
 >>> is_balanced("]")
 False
 >>> is_balanced("Life is a bowl of cherries.")
 True
 >>> is_balanced("Life is a bowl of che{}ies.")
 True
 >>> is_balanced("Life is a bowl of che}{ies.")
 False
 """
 open_to_closed = {"{": "}", "[": "]", "(": ")"}
 stack = []
 for symbol in s:
 if symbol in open_to_closed:
 stack.append(symbol)
 elif symbol in open_to_closed.values() and (
 not stack or open_to_closed[stack.pop()] != symbol
 ):
 return False
 return not stack # stack should be empty


def main():
 s = input("Enter sequence of brackets: ")
 print(f"'{s}' is {'' if is_balanced(s) else 'not '}balanced.")


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

 testmod()
 main()