Problem B: Chemistry

The chemical formula of a molecule M describes its atomic make-up. Chemical formulas obey the following grammar:

      M := G | M G
      G := S | S C
      S := A | '(' M ')'
      C := T | N E
      E := D | D E
      T := '2' | ... | '9'
      N := '1' | ... | '9'
      D := '0' | .. | '9'
      A := U | U L | U L L 
      U := 'A' | .. | 'Z'
      L := 'a' | .. | 'z'
    

The count C represents a multiplier for the subgroup S that precedes it. For example, H2O has two H (hydrogen) and one O (oxygen) atoms, and (AlC2)3Na4 contains 3 Al (aluminum), 6 C (carbon) and 4 Na (sodium) atoms.

Input

The input will contain data for one or more test cases. For each test case, there will be one line of input, containing a valid chemical formula. Each line will have no more than 100 characters.

Output

For each line of input there will be one line of output which is the atomic decomposition of the chemical in the form of a sum as shown in the sample output. The atoms are listed in lexicographical order, and a count of 1 is implied and not explicitly written. There are no blank spaces in the output. All of the counts in the correct output will be representable in 32-bit signed integers.

Sample Input

H2O
(AlC2)3Na4
    

Sample Output

2H+O
3Al+6C+4Na