A8747 | Bracket Sequence

A bracket sequence is a string, containing only characters "(", ")", "\[" and "\]".

A correct 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 "()\[\]", "(\[\])" are correct (the resulting expressions are: "(1)+\[1\]", "(\[1+1\]+1)"), and "\](" and "\[" are not. The empty string is a correct bracket sequence by definition.

A substring $s[l...\ r]$ $(1<=l<=r<=|s|)$ of string $s=s_{1}s_{2}...\ s_{|s|}$ (where $|s|$ is the length of string $s$ ) is the string $s_{l}s_{l+1}...\ s_{r}$ . The empty string is a substring of any string by definition.

You are given a bracket sequence, not necessarily correct. Find its substring which is a correct bracket sequence and contains as many opening square brackets «\[» as possible.

The first and the only line contains the bracket sequence as a string, consisting only of characters "(", ")", "\[" and "\]". It is guaranteed that the string is non-empty and its length doesn't exceed $10^{5}$ characters.

In the first line print a single integer — the number of brackets «\[» in the required bracket sequence. In the second line print the optimal sequence. If there are more than one optimal solutions print any of them.