CF494A.Treasure

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.

马莱克最近发现了一张藏宝图。当他寻找宝藏时，他发现了一扇上锁的门。门上写着一个由字符 '('、')' 和 '#' 组成的字符串 $ s $。门下还附有一份操作手册，说明如何打开这扇门。经过长时间的研究，马莱克成功破译了手册，得知目标是将每个 '#' 替换为一个或多个 ')' 字符，使得最终得到的字符串是“优美的”。

手册中还指出：一个字符串被称为优美的，当且仅当对每个 $ i $（$ 1 \leq i \leq |s| $），在 $ s $ 的前 $ i $ 个字符中，')' 的数量不超过 '(' 的数量，并且整个字符串中 '(' 的总数等于 ')' 的总数。

请帮助马莱克打开这扇门，告诉他每个 '#' 字符应被替换为多少个 ')' 字符。

The first line of the input contains a string s (1 ≤ |s| ≤ 105). Each character of this string is one of the characters '(', ')' or '#'. It is guaranteed that s contains at least one '#' character.

输入的第一行包含一个字符串 $s$（$1 \leq |s| \leq 10^5$）。该字符串的每个字符均为 '('、')' 或 '#' 中的一个。保证 $s$ 中至少包含一个 '#' 字符。

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.

如果不存在将 # 字符替换为某些字符从而得到优美字符串的方法，则输出 -1。否则，对每个字符 #，单独输出一行，该行包含一个正整数，表示该 # 字符必须被替换为的 ) 字符的个数。

如果存在多个可能的答案，你可以输出其中任意一个。

|s| denotes the length of the string s.

$|s|$ 表示字符串 $s$ 的长度。