Mirror Brackets

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

• An empty string is CBS.
• If $s$ is CBS, then ($s$) and [$s$] also are CBS.
• If $s$ and $t$ are CBS, then $st$ also is CBS.
• If a sequence can't be obtained applying the rules given above, then it is not a CBS.

Vasya wrote a correct bracket sequence consisting of brackets "(", ")", "[" and "]". After that Vasya added to some places of the sequence characters "b", "d", "o", "p", "q" and "x". As a result, Vasya got some string $z$.

Now Vasya performs the following operations:

If $z$ has a substring of the form ($s$) (there are no brackets in $s$), then Vasya replaces it with $s$ string's mirror reflection relative to vertical axis. If $z$ contains a substring of the form [$t$] (there are no brackets in $t$ as well), then Vasya replaces it with $t$ string's mirror reflection relative to horizontal axis. For example, substring "(qbpoxd)" will be replaced with "bxoqdp", and substring "[qbpoxd]" will be replaced with "dpboxq".

Vasya performs operations until there are no brackets left in the string.

Calculate by the given $z$ string what result Vasya will have in the end.

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

Print the string Vasya will get in the end.