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.

 def f(t):
    n = t.count('#') - 1
    k = t.rfind('#') + 1
    t = t.replace('#', ')')
    t = [2 * ord(i) - 81 for i in t]

    a = b = c = 0
    for i in t[k: ]:
        b -= i
        c -= i
        if c < 0: c = 0
    if c > 0: return -1
    for i in t[: k]:
        a -= i
        if a < 0: return -1

    if b + a < 0: return -1
    return '1\n' * n + str(b + a + 1)

print(f(input()))