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()

count = 0
store = 0
first = True
ans = False
for c in s:
    if c == "(":
        count += 1
    elif c == ")":
        if store == 0 or count > 0:
            count -= 1
        else:
            store -= 1
        if count < 0:
            print(-1)
            ans = True
            break
    else:
        if not first:
            print(store)
        store = count
        count = 0
        first = False
if not ans:
    if store == 0:
        print(-1)
    else:
        print(store)
  	  	        		 			 	  	   			