Parenthesis are important characters in programming -- they define order of operations and organize information. That is, as long as they are properly balanced. Parenthesis are balanced when opening and closing brackets are match with one another, and are themselves nested within balanced parenthesis.

This is perhaps best illustrated in examples.

• ( ) - balanced: opening is matched with a closing
• ( ( ) - not balanced: one of the opening brackets has no match
• ( [ ) ] - not balanced: the contents inside of ( ) are not balanced

The input file DATA4.txt will contain 5 line, each no more than 255 characters long. Valid characters are any of the three parenthesis types: (), [], {}, and any alphanumeric characters: a-z0-9.

The output file OUT4.txt will contain 5 lines, each stating either "balanced" or "not balanced", for the supplied expressions. Use the exact string output, all lower case, without quotes.

All of the characters but the parenthesis could effectively be ignored. Keep in mind the different types of parenthesis -- an opening bracket needs to be matched with a closing bracket of the same type.

abc
([{a}b]c)
)(
([)]
{abc]
        

balanced
balanced
not balanced
not balanced
not balanced