Brackets

We define a regular brackets sequence by the following inductive rules:

• the empty sequence is a regular brackets sequence;
• if $s$ is a regular brackets sequence, then $(s)$ and $[s]$ are regular brackets sequences;
• if $a$ and $b$ are regular brackets sequences, then their concatenation $ab$ is a regular brackets sequence;
• no other sequence is a regular brackets sequence.

For example, all of the following are regular brackets sequences:

(), [], (()), ()[], ()[()]

while none of the following are:

(, ], )(, ([)], ([(]

Given a brackets sequence $a_1 a_2 \dots a_n$, find the length of the longest regular brackets sequence that is a subsequence of it. That is, find the largest $m$ for which there exist indices $1 \le i_1 < i_2 < \dots < i_m \le n$ such that $a_{i_1} a_{i_2} \dots a_{i_m}$ is a regular brackets sequence.

The input contains multiple test cases. Each test case is a single line consisting only of the characters (, ), [, and ]; every such line has length between $1$ and $100$, inclusive.

The input ends with a line containing the single word end, which must not be processed.

For each test case, print on its own line the length of the longest regular brackets subsequence.

For the sequence ([([]])], one of the longest regular brackets subsequences is [([])], which has length $6$.