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.
k=input()
r,m,n=0,0,0
i=0
while i<len(k):
    if k[i]=='(':
        r+=1
        
    if k[i]==')':
        m+=1
        
    if k[i]=='#':
        if r==0:
            print(-1)
            break
        else:
            if i==k.rindex('#'):
                q=i+1
                while q<len(k):
                    
                    if k[q]=='(':
                        r+=1
                    if k[q]==')':
                        m+=1
                    q+=1  
                if r<=m:
                    print(-1)
                    break
                                   
               
                o=r-m
                print(o)
                break
            else:
                o=r-2
                print(o)
                m+=o

    i+=1        
                    