"THE MOBILE" (SWEDEN)
 


 
 
 

In figure 1 you can see a mobile in perfect balance. The mobile have five weights 1 kg, 2 kg ... 5 kg. The distance between two marks is 1 m. You can check the balance through this calculation

-3·3 + -1·5 + 2·(1+2+4)=0
-2·1 + -1·2 + 1·4=0

When you get a mobile problem you will get the structure of the mobile from a character string. The mobile in figure 1 is described in this way

(-3,-1,2(-2,-1,1))

You have to calculate such weights so the mobile is in perfect balance and give the answer as another character string. From figure 1 with the five weights the answer is

(3,5,(1,2,4))

You will now write a program reading a description of a mobile from an input file, calculate the weights and writing the answer to an output file.

Here you will have two additional examples with input and output string.
 


 
 

Input data (file MOBILE.IN)
(-3(-1(-1(-1,1,2),3),2),3(-2,1,2),6(-2,3))

Output data (file MOBILE.OUT)
((((8,6,1),5),10),(9,4,7),(3,2))
 
 

Input data (file MOBILE.IN)
(-8,-4(-5,-3,-1,1),-2(-1,1,3),2(-1(-3,-2,1(-2,1,3)),1,3),6)

Output data (file MOBILE.OUT)
(10,(1,2,4,15),(14,5,3),((6,8,(16,11,7)),9,13),12)


TEST CASES