P1010 [NOIP 1998 Junior] Powers of Two

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 $2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)$.

One line containing a positive integer $n$.

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

- Constraints: For $100\%$ of the testdata, $1 \le n \le 2 \times {10}^4$. - NOIP 1998 Junior, Problem 3. Translated by ChatGPT 5