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.
arr = list(input().strip())
left_parenthesis, right_parenthesis = arr.count("("), arr.count(")")
hashtag = len(arr) - left_parenthesis - right_parenthesis

total_diff = left_parenthesis - right_parenthesis
for i in range(hashtag):
    if i == hashtag-1:
        last_total = total_diff
    else:
        last_total = 1
    total_diff -= last_total
    if last_total == 0 or total_diff < 0: print("-1")
    else: print(last_total)
        
 		    			  		    	 	    			 	