Description

Any positive integer can be expressed as a sum of powers of $2$. For example, $137=2^7+2^3+2^0$.

We also agree to write exponents using parentheses, i.e., $a^b$ can be written as $a(b)$.

Thus, $137$ can be written as $2(7)+2(3)+2(0)$.

Furthermore, $7= 2^2+2+2^0$ (where $2^1$ is written as $2$), and $3=2+2^0$.

Therefore, the final expression for $137$ is $2(2(2)+2+2(0))+2(2+2(0))+2(0)$.

Another example: $1315=2^{10} +2^8 +2^5 +2+1$.

Thus, the final expression for $1315$ is $2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)$.

Input Format

One line containing a positive integer $n$.

Output Format

Output the agreed "0, 2" representation of $n$ (no spaces are allowed in the expression).

1315

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

Hint

• Constraints: For $100\%$ of the testdata, $1 \le n \le 2 \times {10}^4$.
• NOIP 1998 Junior, Problem 3.

Translated by ChatGPT 5