P1832 A+B Problem (Another Upgrade)

The title is meant to attract you to click. In fact, this problem is still quite easy.

- $1+1=?$ Obviously $2$. - $a+b=?$ See P1001, don't thank me. - Goldbach's conjecture seems to be everywhere. _The above is purely a personal rant._ Given a positive integer $n$, find the total number of ways to express it as a sum of prime numbers. The order of addends does not matter.

One line containing a positive integer $n$.

One line containing an integer representing the total number of ways.

### Sample Explanation There are the following three ways: - $7=7$. - $7=2+5$. - $7=2+2+3$. ### Constraints - For $30\%$ of the testdata, $1 \le n \le 10$. - For $100\%$ of the testdata, $1 \le n \le 10^3$. Translated by ChatGPT 5