Kris is playing a game, which involves removing stones from a pile that initially consists of $n$ stones. He is given a set of prime numbers $P$, and each time he is able to choose one $p$ from $P$ and remove $m\bmod p$ stones from the pile, where $m$ stands for the number of stones remaining in the pile. The game finishes once no stone is left in the pile, and he wants to put an end to the game using least number of rounds possible.
Given $N$, you are expected to calculate the minimum rounds $a_n$ required to finish the game starting with a pile of $n$ stones for all $1\le n\le N$. And if there is no possible solution for certain $n$, we set $a_n=0$. And in order to prevent large output, you only need to print $\left(\sum_{1\le n\le N}a_n\times 23333^{N-n}\right)\bmod 2^{64}$.