This is challenge version of A Very Easy Problem!. Given integer i, Your task is to convert integer i into http://www.spoj.com/problems/EASYPROB/ format.

Score is the length of your source.

Input

There are multiple test cases, each line contain an integer i(0 < i < 2⁶⁴). Process input until EOF.

Output

For each case, output the converted number in separate line.

Example

Input:
137

1315

Output:
137=2(2(2)+2+2(0))+2(2+2(0))+2(0)

1315=2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)

See also: Another problem added by Tjandra Satria Gunawan