Malek has recently found a treasure map. While he was looking for a treasure he found a locked door. There was a string $*s*$ written on the door consisting of characters '(', ')' and '#'. Below there was a manual on how to open the door. After spending a long time Malek managed to decode the manual and found out that the goal is to replace each '#' with one or more ')' characters so that the final string becomes beautiful.

Below there was also written that a string is called beautiful if for each $*i*$ ($1 ≤ *i* ≤ |*s*|$) there are no more ')' characters than '(' characters among the first $*i*$ characters of $*s*$ and also the total number of '(' characters is equal to the total number of ')' characters.

Help Malek open the door by telling him for each '#' character how many ')' characters he must replace it with.

Input

The first line of the input contains a string $*s*$ ($1 ≤ |*s*| ≤ 10^{5}$). Each character of this string is one of the characters '(', ')' or '#'. It is guaranteed that $*s*$ contains at least one '#' character.

Output

If there is no way of replacing '#' characters which leads to a beautiful string print $- 1$. Otherwise for each character '#' print a separate line containing a positive integer, the number of ')' characters this character must be replaced with.

If there are several possible answers, you may output any of them.

Note

$|*s*|$ denotes the length of the string $*s*$.