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()  # ������
l = len(s)
d = []

a = 0
b = 0
for i in range(l):
    if s[i] == '(':
        a += 1
    elif s[i] == ')':
        b += 1
    else:
        d.append(a-b)  # ����������� ��������� ��������

n = a-b

if n <= 0:  # ���������� ���������� ������
    print(-1)
else:
    ans = []
    pos = len(d)-1
    while (pos > -1) and (n > 0):
        m = min(d[pos], n-pos)
        ans.insert(0, m)
        n -= m
        pos -= 1
    if n > 0:
        print(-1)
    else:
        for i in ans:
            print(i)