Mirror Brackets

Let's recall what a correct bracket sequence (CBS) is.

• An empty string is a CBS.
• If $s$ is a CBS, then ($s$) and [$s$] are also CBS.
• If $s$ and $t$ are CBS, then $st$ is also a CBS.
• A sequence that cannot be obtained by the rules above is not a CBS.

Vasya wrote a correct bracket sequence using the brackets "(", ")", "[" and "]". Then he inserted some of the characters "b", "d", "o", "p", "q" and "x" at various places in the sequence, which produced a string $z$.

Vasya repeats the following operations.

If $z$ contains a substring of the form ($s$) (where $s$ has no brackets), he replaces it with the mirror reflection of $s$ across the vertical axis. If $z$ contains a substring of the form [$t$] (where $t$ has no brackets), he replaces it with the mirror reflection of $t$ across the horizontal axis. For example, the substring "(qbpoxd)" becomes "bxoqdp", and the substring "[qbpoxd]" becomes "dpboxq".

Vasya keeps performing these operations until no brackets remain. Given $z$, find the final string.

The only line contains the string $z$, whose length does not exceed $10^5$. The string consists of the characters "(", ")", "[", "]", "b", "d", "o", "p", "q" and "x". It is guaranteed that the brackets in $z$ form a correct bracket sequence. It is also guaranteed that the input contains at least one letter.

Print the final string that Vasya gets.