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()
ans = []
count = 0
last_pos = s.rfind('#')
for i, c in enumerate(s):
    if c == '(':
        count += 1
    elif c == ')':
        count -= 1
    elif c == '#' and i == last_pos:
        num = max(1, s.count('(') * 2 - len(s) + 1)
        count -= num
        ans.append(num)
    else:
        count -= 1
        ans.append(1)
    if count < 0:
        print(-1)
        break
else:
    for t in ans:
        print(t)
    

