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.
#!/usr/bin/env python3

s = input()
count = 0
res = []
last = s.rfind("#")

for i, c in enumerate(s):
    if c == '(':
        count += 1
    elif c == ')':
        count -= 1
    else:
        if i < last:
            res.append(1)
            count -= 1
        else:
            num = max(1, 1 + s.count("(") - s.count("#") - s.count(")"))
            res.append(num)
            count -= num
    if count < 0:
        res = []
        print(-1)
        break
for i in res:
    print(i)
