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))

Input and Output

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.

• If there are n weights in the mobile you must use the weights from 1 kg to n kg exactly once
• The mobile must be in perfect balance.
• n £ 17
• There will be no more than 7 attachments hanging from any of the bars. The mobile on fig.1 has 2 bars with 3 attachments hanging from each.
• The input string will be given as a single line in the input file MOBILE.IN. All numbers are integers which values are between -50 and 50 (inclusive).
• The output string must be given as a single line in the output file MOBILE.OUT, without spaces.
• You can assume that for each given test data at least one solution exists. If more than one solution is possible, you must output one of them.

Sample Input 1

(-3(-1(-1(-1,1,2),3),2),3(-2,1,2),6(-2,3))

Sample Output 1

((((8,6,1),5),10),(9,4,7),(3,2))

Figure 1

Sample Input 2

(-8,-4(-5,-3,-1,1),-2(-1,1,3),2(-1(-3,-2,1(-2,1,3)),1,3),6)

Sample Output 2

(10,(1,2,4,15),(14,5,3),((6,8,(16,11,7)),9,13),12)

Figure 2