Longest Valid Bracket Substring

Given a string consisting only of the characters (, ), [ and ], find the length of its longest contiguous substring that is a valid bracket matching sequence.

A bracket matching sequence is defined as follows:

• () and [] are valid sequences.
• If A is a valid sequence, then (A) and [A] are also valid sequences.
• If both A and B are valid sequences, then their concatenation AB is also a valid sequence.

A substring of a string is a contiguous block of characters from that string. The empty string is also considered a substring.

Your task is to compute the length of the longest substring that is a valid bracket matching sequence.

Note: If no non-empty valid sequence exists, output 0.

inputFormat

The input consists of a single line containing a string composed only of the characters (', ')', '[' and ']'.

outputFormat

Output a single integer representing the length of the longest valid bracket substring.

sample

([])

4