A bracket sequence is a string consisting of characters '(' and/or ')'. A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example:

• bracket sequences "()()" and "(())" are regular (they can be transformed into "(1)+(1)" and "((1+1)+1)", respectively);
• bracket sequences ")(", "(" and ")" are not regular.

You are given a bracket sequence $s$; let's define its length as $n$. Your task is to find a regular bracket sequence $t$ of length $2n$ such that $s$ does not occur in $t$ as a contiguous substring, or report that there is no such sequence.