A Balanced World

The world must be well balanced — like positive and negative, light and dark, and left and right brackets.

Jeongmin's task is to write a program that, given a string, decides whether the brackets inside it are balanced.

A string may contain two kinds of brackets: round brackets ( ) and square brackets [ ]. A string is balanced when all of the following hold:

• Every left round bracket ( pairs only with a right round bracket ).
• Every left square bracket [ pairs only with a right square bracket ].
• Every right bracket has a matching left bracket somewhere before it.
• Every pairing is one-to-one; a single bracket cannot pair with more than one other bracket.
• For any two matched brackets, the substring between them must also be balanced.

Help Jeongmin decide whether each given string is balanced.

The input consists of several lines. Except for its last character, each line (string) consists of English letters, spaces, round brackets ( ), and square brackets [ ], always ends with a period ., and is at most 100 characters long.

The input ends with a line containing a single period .; this terminating line is not processed.

For each string, print yes on its own line if it is balanced, or no otherwise.

A string that contains no brackets at all (for example, a string of only spaces) is also considered balanced.