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.
The first line of the input contains a string *s* (1 ≤ |*s*| ≤ 10<sup class="upper-index">5</sup>). Each character of this string is one of the characters '(', ')' or '#'. It is guaranteed that *s* contains at least one '#' character.
s = input()
hash = 0
left,right = 0,0
sh = s.count('#')
sl = s.count('(')
sr = s.count(')')
if sh+sr<=sl:
    for i in s:
        if i=='(':
            left+=1
        elif i==')':
            right+=1
        else:
            hash+=1
            if left>right:
                print(left-right)
                hash-=1
                right = left = 0
            else:
                print(1)
                right+=1
                hash-=1
else:
    print(-1)