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.
import sys

def main():
    for ln in sys.stdin:
        s=ln.strip()
        for x in solve(s):
            print(x)

def solve(s):
    print()
    print(s)

    ans=[]
    n=len(s)
    r=l=h=0
    for i in range(n):
        if s[i]=='(':
            r+=1
        elif s[i]==')':
            l+=1
        else:
            h+=1
    if r<=l:
        return [-1]
    for i in range(n-1,-1,-1):
        if s[i]==')':
            r-=1
            l-=1
        elif s[i]=='#':
            if r==0:
                return [-1]
            r-=1
            h-=1
            x=r-l-h
            if r-x>0:
                r-=x
            else:
                x=0
            ans.append(1+x)

    ans=ans[::-1]
    return ans

#print(solve('#'))
#print(solve('(#)'))
#print(solve('((#)'))
#
#print(solve('(((#)((#)'))
#
#print(solve('()((#((#(#()'))
#print(solve('((((#((#())'))

main()
