#### Nested Brackets

R
p
```"""
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()
```