Given a string of parentheses, we must turn it into a well formed string by changing as few characters as possible (we cannot delete or insert characters). There are three kinds of parentheses: regular (), brackets \[\] and curly brackets \{\}. Each pair has an opening ('(', '\[' and '\{' respectively) and a closing (')', '\]' and '\}') character. A well formed string of parentheses is defined by the following rules: \begin{itemize} \item The empty string is well formed. \item If \textbf{s} is a well formed string, (\textbf{s}), \[\textbf{s}\] and \{\textbf{s}\} are well formed strings. \item If \textbf{s} and \textbf{t }are well formed strings, the concatenation \textbf{st }is a well formed string. \end{itemize} As examples, "(\[\{\}\])", "" and "()\{\}\[\]" are well formed strings and "(\[\}\]", "(\[)\]" and "\{" are malformed strings. For the given string of parentheses find the minimum number of characters that need to be changed to make it into a well formed string. \InputFile Each line contains the string with even number of symbols '(', ')', '\[', '\]', '\{', '\}'. The length of each line is no more than \textbf{50}. \OutputFile For each input string print in a separate line the minimum number of characters that need to be changed to make it into a well formed string.