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.
# read input string
s = input()

# count the number of open and close parentheses
n_open = s.count('(')
n_close = s.count(')')

# calculate the number of replacements needed for each '#'
replacements = []
count = 0
for char in s:
    if char == '(':
        count += 1
    elif char == ')':
        count -= 1
    else:
        needed = n_close - count
        if needed <= 0 or (n_open - count) <= 0:
            # no way to make the string beautiful
            print("-1")
            exit()
        replacements.append(needed)
        count += needed

# print the number of replacements needed for each '#'
for r in replacements:
    print(r)
