Description

Any positive integer can be expressed as a sum of powers of 2. For example:

137 = 2^7 + 2^3 + 2^0

By convention, exponents are enclosed in parentheses, meaning a^b can be written as a(b). Thus, 137 can be represented as:

2(7) + 2(3) + 2(0)

Further breaking it down:
7 = 2^2 + 2 + 2^0 (where 2^1 is written simply as 2)
3 = 2 + 2^0

Therefore, the final representation of 137 becomes:

2(2(2)+2+2(0)) + 2(2+2(0)) + 2(0)

Another example:

1315 = 2^10 + 2^8 + 2^5 + 2 + 1

So, 1315 is ultimately represented as:

2(2(2+2(0))+2) + 2(2(2+2(0))) + 2(2(2)+2(0)) + 2 + 2(0)

Input Format

A positive integer n (n ≤ 20000).

Output Format

A single line containing the representation of n using the specified 0 and 2 notation (no spaces allowed in the output).

137

2(2(2)+2+2(0))+2(2+2(0))+2(0)