Treasure

得你一个包含"("和"#"的序列，'#'需要转换为k个右括号 ( k > 0 )，那么这个表达式的括号能否在你转化后匹配，如果可以，输出每一个'#'转化的右括号数 k 的值；如果不能，就输出 −1 可能有很多组满足的情况只需输出一组即可 ~~Special Judge 万岁~~

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.

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.

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.

(((#)((#)

1
2

()((#((#(#()

2
2
1

#

-1

(#)

-1

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