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A9714. Treasure

编程题 普及/提高-

题目描述

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.

输入格式

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.

输出格式

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.

输入输出样例

输入 #1
(((#)((#)
输出 #1
1
2
输入 #2
()((#((#(#()
输出 #2
2
2
1
输入 #3
#
输出 #3
-1
输入 #4
(#)
输出 #4
-1

说明/提示

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