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,r,l,t=input()+"1",0,0,1
a=[]
for i in range(len(s)-1):
    if s[i]=="(":
        r+=1
    elif s[i]==")":
        l+=1
    elif r>l:
        if s[i+1]=="(" or r==1:
            a.append(str(r-l))
            l+=r-l
        else:
            a.append(str(r-l-1))
            l+=r-l-1
    else:
        print("-1")
        t=0
        break
    if l>r:
        print("-1")
        t=0
        break
if t:
    print("\n".join(a))